4904:
6192:
47:
5734:
1617:
20:
5744:
2094:(LQG) it is possible to associate a geometrical interpretation with the microstates: these are the quantum geometries of the horizon. LQG offers a geometric explanation of the finiteness of the entropy and of the proportionality of the area of the horizon. It is possible to derive, from the covariant formulation of full quantum theory (
2816:, which says the entropy of a system must go to zero as the temperature goes to absolute zero is also not a universal law. However the systems that fail the classical third law have not been realized in practice, leading to the suggestion that the extremal black holes may not represent the physics of black holes generally.
2110:. The current accepted microstate ensemble for black holes is the microcanonical ensemble. The partition function for black holes results in a negative heat capacity. In canonical ensembles, there is limitation for a positive heat capacity, whereas microcanonical ensembles can exist at a negative heat capacity.
2964:
While black hole thermodynamics (BHT) has been regarded as one of the deepest clues to a quantum theory of gravity, there remain some philosophical criticisms that it “is often based on a kind of caricature of thermodynamics” and "it’s unclear what the systems in BHT are supposed to be", leading to
2663:
near the exterior of black holes, is not useful. The GSL allows for the application of the law because now the measurement of interior, common entropy is possible. The validity of the GSL can be established by studying an example, such as looking at a system having entropy that falls into a bigger,
2675:
However, on the topic of black hole formation, the question becomes whether or not the generalized second law of thermodynamics will be valid, and if it is, it will have been proved valid for all situations. Because a black hole formation is not stationary, but instead moving, proving that the GSL
2828:
The four laws of black hole mechanics suggest that one should identify the surface gravity of a black hole with temperature and the area of the event horizon with entropy, at least up to some multiplicative constants. If one only considers black holes classically, then they have zero temperature
2968:
These criticisms triggered a fellow skeptic to reexamine "the case for regarding black holes as thermodynamic systems", with particular attention paid to "the central role of
Hawking radiation in permitting black holes to be in thermal contact with one another" and "the interpretation of Hawking
2654:
in an isolated system will be greater than or equal to 0 for a spontaneous process, suggesting a link between entropy and the area of a black hole horizon. However, this version violates the second law of thermodynamics by matter losing (its) entropy as it falls in, giving a decrease in entropy.
1714:. If black holes carried no entropy, it would be possible to violate the second law by throwing mass into the black hole. The increase of the entropy of the black hole more than compensates for the decrease of the entropy carried by the object that was swallowed.
2819:
A weaker form of the classical third law known as the "unattainability principle" states that an infinite number of steps are required to put a system in to its ground state. This form of the third law does have an analog in black hole physics.
2664:
non-moving black hole, and establishing upper and lower entropy bounds for the increase in the black hole entropy and entropy of the system, respectively. One should also note that the GSL will hold for theories of gravity such as
2600:, is the change in energy (proportional to mass). Although the first term does not have an immediately obvious physical interpretation, the second and third terms on the right side represent changes in energy due to rotation and
1889:
3007:
of nature, which asserts that consistent theories of gravity and quantum mechanics must be lower-dimensional. Though not yet fully understood in general, the holographic principle is central to theories like the
2256:
2087:, viewed as the most far-from-extremal black hole, the relationship between micro- and macrostates has not been characterized. Efforts to develop an adequate answer within the framework of string theory continue.
2655:
However, generalizing the second law as the sum of black hole entropy and outside entropy, shows that the second law of thermodynamics is not violated in a system including the universe beyond the horizon.
2658:
The generalized second law of thermodynamics (GSL) was needed to present the second law of thermodynamics as valid. This is because the second law of thermodynamics, as a result of the disappearance of
1998:
2688:. This discipline does not exist so the GSL can be assumed to be useful in general, as well as for prediction. For example, one can use the GSL to predict that, for a cold, non-rotating assembly of
1774:
2890:
1336:
2943:
2043:
Although
Hawking's calculations gave further thermodynamic evidence for black hole entropy, until 1995 no one was able to make a controlled calculation of black hole entropy based on
2481:
2748:
1939:
1171:
1116:
1061:
5629:
868:
821:
736:
689:
601:
554:
2518:
772:
640:
2567:
2486:
This "law" was superseded by
Hawking's discovery that black holes radiate, which causes both the black hole's mass and the area of its horizon to decrease over time.
2347:
2303:
2778:
1006:
2395:
2636:
1814:
2598:
505:
2798:
2706:
2419:
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2327:
2279:
2026:
1912:
844:
797:
712:
665:
577:
530:
6650:
3803:
Wu, Wang, Yang, Zhang, Shao-Feng, Bin, Guo-Hang, Peng-Ming (17 November 2008). "The generalized second law of thermodynamics in generalized gravity theories".
6374:
2969:
radiation close to the black hole as a gravitationally bound thermal atmosphere", ending with the opposite conclusion -- "stationary black holes are not
1788:
relationship between energy, temperature and entropy, Hawking was able to confirm
Bekenstein's conjecture and fix the constant of proportionality at
3856:
2106:
and is done for non-extremal black holes. There seems to be also discussed the calculation of
Bekenstein–Hawking entropy from the point of view of
2008:. The subscript BH either stands for "black hole" or "Bekenstein–Hawking". The black hole entropy is proportional to the area of its event horizon
1822:
1646:
6342:
4675:
4284:"Are We All Wrong About Black Holes? Craig Callender worries that the analogy between black holes and thermodynamics has been stretched too far"
1347:
1776:
as the constant of proportionality, asserting that if the constant was not exactly this, it must be very close to it. The next year, in 1974,
4985:
1235:
2184:
4990:
6326:
2178:
For perturbations of stationary black holes, the change of energy is related to change of area, angular momentum, and electric charge by
469:
2895:
From the first law of black hole mechanics, this determines the multiplicative constant of the
Bekenstein–Hawking entropy, which is (in
6287:
5709:
5366:
1721:
conjectured that black holes should have an entropy proportional to the area of the event horizon, where by the same year, he proposed
2040:, which relates the entanglement entropy of a boundary conformal field theory to a specific surface in its dual gravitational theory.
6229:
5780:
4362:
Ofer
Aharony; Steven S. Gubser; Juan Maldacena; Hirosi Ooguri; Yaron Oz (2000). "Large N field theories, string theory and gravity".
1325:
6297:
5921:
5304:
5130:
5030:
3053:
2953:
6572:
1358:
6588:
6433:
5886:
3235:
4283:
1948:
6556:
4807:
4649:
3414:
1731:
928:
2847:
6596:
6536:
1639:
1226:
895:
462:
340:
4780:
2956:
can be utilized to calculate the entropy for a black hole in any covariant theory for gravity, known as the Wald entropy.
6686:
6660:
2051:" theorems appeared to suggest that black holes could have only a single microstate. The situation changed in 1995 when
278:
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6645:
6406:
5346:
1410:
1384:
905:
359:
6366:
6195:
5435:
311:
3616:
Ashtekar, Abhay; Baez, John; Corichi, Alejandro; Krasnov, Kirill (1998). "Quantum
Geometry and Black Hole Entropy".
1690:, the effort to understand the statistical mechanics of black holes has had a deep impact upon the understanding of
6441:
6398:
6267:
5911:
5808:
5430:
2905:
1463:
934:
333:
5315:
4308:
Wallace, David (November 2018). "The case for black hole thermodynamics part I: Phenomenological thermodynamics".
6457:
5351:
5147:
1632:
6655:
6512:
6101:
5969:
5573:
5254:
4893:
1563:
95:
1458:
6564:
6222:
5984:
5896:
5858:
5773:
5341:
5216:
2677:
2443:
2037:
1538:
1311:
288:
2434:
6350:
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5747:
5259:
5162:
4950:
2647:
2534:
1707:
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126:
116:
5269:
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5528:
5518:
2605:
131:
121:
4310:
Studies in
History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics
6358:
6277:
6272:
5964:
5249:
5201:
5184:
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4641:
2685:
2669:
1415:
1379:
157:
91:
4706:
1453:
6604:
6282:
6077:
6054:
6004:
5704:
5120:
4868:
4800:
3752:
Bekenstein, Jacob D. (1974-06-15). "Generalized second law of thermodynamics in black hole physics".
3259:
3145:
2398:
1208:
956:
402:
215:
205:
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6382:
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6085:
5766:
5381:
2711:
2084:
2080:
2075:. Their calculation was followed by many similar computations of entropy of large classes of other
4415:
Callaway, D. (1996). "Surface tension, hydrophobicity, and black holes: The entropic connection".
4003:
2808:
The third law of black hole thermodynamics is controversial. Specific counterexamples to called
1917:
6449:
6390:
6334:
6121:
5931:
5863:
5823:
5558:
5094:
5057:
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4955:
4873:
4770:
4271:. Guide to the Philosophy of Cosmology, editors: A. Ijjas and B. Loewer. Oxford University Press.
3954:
3441:
Bhattacharya, Sourav (2007). "Black-Hole No-Hair
Theorems for a Positive Cosmological Constant".
1620:
1448:
1245:
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1016:
948:
887:
423:
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78:
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5803:
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5476:
5461:
5320:
5013:
4827:
3104:
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2609:
2497:
2028:. The fact that the black hole entropy is also the maximal entropy that can be obtained by the
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1553:
1270:
354:
108:
83:
28:
1473:
754:
619:
6414:
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5828:
5466:
5279:
5023:
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3004:
2552:
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2288:
2102:
and the distribution that yields Hawking entropy. The calculation makes use of the notion of
2044:
2033:
1695:
1679:
1488:
1065:
378:
224:
73:
2988:
and Hawking have shown that black hole thermodynamics is more general than black holes—that
2753:
2032:(wherein the Bekenstein bound becomes an equality) was the main observation that led to the
976:
6681:
6062:
5737:
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5196:
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3164:
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145:
8:
6528:
6520:
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5543:
5513:
5471:
5425:
5062:
4928:
4923:
4853:
3834:
3502:
Strominger, A.; Vafa, C. (1996). "Microscopic origin of the Bekenstein-Hawking entropy".
2813:
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2538:
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258:
171:
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4143:
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4029:
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3826:
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3717:
3639:
3578:
3525:
3464:
3373:
3324:
3260:"Artificial event horizon emits laboratory analogue to theoretical black hole radiation"
3168:
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1508:
487:
6116:
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5402:
5274:
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4371:
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4343:
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4237:
4204:
4192:
4168:
4129:
4117:
4072:
4037:
4015:
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3927:
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3874:
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3812:
3785:
3731:
3703:
3670:
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3625:
3598:
3564:
3537:
3511:
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3420:
3392:
3359:
3336:
3215:
3180:
3154:
3122:
3086:
2996:
2949:
2833:, zero entropy, and the laws of black hole mechanics remain an analogy. However, when
2783:
2691:
2665:
2404:
2356:
2312:
2264:
2011:
1942:
1897:
1602:
1265:
1260:
1213:
829:
782:
697:
650:
562:
515:
445:
429:
316:
268:
253:
243:
52:
46:
4393:
3980:
6580:
6252:
6161:
6156:
5936:
5901:
5548:
5538:
5533:
5233:
5221:
5174:
5115:
5084:
5074:
5008:
4756:
4702:
4645:
4550:
4450:
4401:
4242:
4173:
4155:
4098:
4041:
3984:
3932:
3914:
3842:
3789:
3777:
3735:
3590:
3533:
3488:
3476:
3424:
3410:
3244:
3219:
3126:
3028:
2896:
2838:
2834:
2155:
2103:
2099:
2083:, and the result always agreed with the Bekenstein–Hawking formula. However, for the
2052:
1781:
1687:
1597:
1558:
1548:
1120:
918:
746:
248:
238:
180:
4748:
4628:
4513:
4347:
4060:
3655:
3602:
3340:
3232:
3184:
2047:, which associates entropy with a large number of microstates. In fact, so called "
6490:
6262:
5979:
5699:
5659:
5407:
5356:
5211:
5125:
4918:
4888:
4744:
4698:
4616:
4587:
4575:
4538:
4501:
4462:
4442:
4389:
4335:
4232:
4222:
4163:
4147:
4090:
4033:
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3922:
3904:
3830:
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3615:
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3541:
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2131:
2029:
1718:
1518:
1503:
1443:
1438:
1255:
1250:
900:
368:
233:
4261:
3669:
Bianchi, Eugenio (2012). "Entropy of Non-Extremal Black Holes from Loop Gravity".
3472:
6238:
6166:
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5284:
5191:
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4481:
3308:
3283:
3239:
3016:
2830:
2672:, or Braneworld gravity, because the conditions to use GSL for these can be met.
2494:
It is not possible to form a black hole with vanishing surface gravity. That is,
2422:
2306:
2167:
2143:
2048:
1777:
1722:
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1468:
1316:
970:
611:
434:
195:
162:
4775:
4339:
3955:"Does the third law of black hole thermodynamics really have a serious failure?"
3586:
2812:
fail to obey the rule. The classical third law of thermodynamics, known as the
6302:
6136:
5634:
5619:
5386:
5325:
5169:
4843:
3647:
3406:
2965:
the conclusion -- "the analogy is not nearly as good as is commonly supposed".
2135:
2127:
2072:
1523:
1293:
393:
273:
210:
200:
68:
38:
3387:
Van Raamsdonk, Mark (31 August 2016). "Lectures on Gravity and Entanglement".
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6111:
6021:
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4159:
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3918:
3781:
3276:
2646:
The second law is the statement of Hawking's area theorem. Analogously, the
2064:
2060:
2001:
1884:{\displaystyle S_{\text{BH}}={\frac {k_{\text{B}}A}{4\ell _{\text{P}}^{2}}},}
1785:
1675:
1592:
910:
479:
440:
152:
4542:
4118:"A general derivation and quantification of the third law of thermodynamics"
3773:
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5843:
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5491:
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holds is difficult. Proving the GSL is generally valid would require using
1543:
1528:
1478:
961:
4454:
3354:
Majumdar, Parthasarathi (1999). "Black Hole Entropy and Quantum Gravity".
6106:
5689:
5639:
5593:
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5371:
5310:
5035:
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3033:
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1498:
306:
4227:
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3277:
Charlie Rose: A conversation with Dr. Stephen Hawking & Lucy Hawking
1784:
corresponding to a certain temperature (Hawking temperature). Using the
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5152:
5089:
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4731:
4665:
4620:
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4376:
3555:
Rovelli, Carlo (1996). "Black Hole Entropy from Loop Quantum Gravity".
3516:
3332:
3211:
3159:
2123:
1672:
1587:
1533:
24:
4209:
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3691:
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3455:
3364:
2251:{\displaystyle dE={\frac {\kappa }{8\pi }}\,dA+\Omega \,dJ+\Phi \,dQ,}
2036:. This area relationship was generalized to arbitrary regions via the
6126:
5994:
5906:
5878:
5714:
5361:
5264:
5052:
5047:
4717:
Page, Don (2005). "Hawking Radiation and Black Hole Thermodynamics".
4579:
2549:
constant for thermal equilibrium for a normal system is analogous to
2537:, which states that the temperature is constant throughout a body in
185:
19:
6034:
5833:
5624:
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3003:
used the laws of black hole thermodynamics to argue for a general
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2660:
2651:
1711:
1660:
407:
3015:
There are also connections between black hole entropy and fluid
5684:
5674:
5654:
5376:
4975:
4965:
4479:
4316:. Philosophy of Modern Physics, Volume 64, Pages 52-67: 52–67.
2282:
4785:
4521:
Bekenstein, Jacob D. (April 1973). "Black holes and entropy".
2098:) the correct relation between energy and area (1st law), the
4659:
Hawking, Stephen W. (1994). "The Nature of Space and Time".
2126:
are believed to satisfy. The laws, analogous to the laws of
4259:
383:
3198:
Bekenstein, A. (1972). "Black holes and the second law".
2837:
are taken into account, one finds that black holes emit
2541:. It suggests that the surface gravity is analogous to
1993:{\displaystyle \ell _{\text{P}}={\sqrt {G\hbar /c^{3}}}}
1769:{\displaystyle {\frac {\ln {2}}{0.8\pi }}\approx 0.276}
4635:
4558:
Hawking, Stephen W. (1974). "Black hole explosions?".
2885:{\displaystyle T_{\text{H}}={\frac {\kappa }{2\pi }}.}
2569:
constant over the horizon of a stationary black hole.
3802:
3143:
Bousso, Raphael (2002). "The Holographic Principle".
3138:
3136:
2948:
which is the entropy of the black hole in Einstein's
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2714:
2694:
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2500:
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calculated the right Bekenstein–Hawking entropy of a
2014:
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4480:Bardeen, J. M.; Carter, B.; Hawking, S. W. (1973).
4253:
3692:"Microcanonical description of (micro) black holes"
2113:
4262:"Black Hole Thermodynamics: More Than an Analogy?"
4116:Masanes, LluĂs; Oppenheim, Jonathan (2017-03-14).
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2154:The laws of black hole mechanics are expressed in
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1667:is the area of study that seeks to reconcile the
6673:
4115:
4061:""Nernst theorem" and black hole thermodynamics"
4004:"Gravitation, thermodynamics and quantum theory"
6343:Black Holes and Baby Universes and Other Essays
3077:Carlip, S (2014). "Black Hole Thermodynamics".
3501:
2977:thermodynamic systems, in the fullest sense."
6223:
5774:
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3868:
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3386:
2938:{\displaystyle S_{\text{BH}}={\frac {A}{4}}.}
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3855:: CS1 maint: multiple names: authors list (
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2612:, which contains on its right side the term
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5367:Magnetospheric eternally collapsing object
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4771:Bekenstein-Hawking entropy on Scholarpedia
4676:"On the quantum structure of a black hole"
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3926:
3908:
3890:
3816:
3725:
3707:
3674:
3629:
3568:
3515:
3454:
3431:
3396:
3363:
3158:
3108:
3090:
3079:International Journal of Modern Physics D
2523:
2238:
2225:
2212:
4636:Hawking, S. W.; Ellis, G. F. R. (1973).
4414:
3943:
3353:
3233:"First Observation of Hawking Radiation"
3054:List of loop quantum gravity researchers
2954:Quantum field theory in curved spacetime
2149:
1686:led to the development of the theory of
18:
6573:Stephen Hawking: Master of the Universe
6327:The Large Scale Structure of Space–Time
4658:
4638:The Large Scale Structure of Space–Time
4594:
4557:
4482:"The four laws of black hole mechanics"
4307:
3689:
3668:
3554:
3306:
2476:{\displaystyle {\frac {dA}{dt}}\geq 0.}
6674:
6589:Into the Universe with Stephen Hawking
4601:Communications in Mathematical Physics
4486:Communications in Mathematical Physics
4281:
3313:Communications in Mathematical Physics
3297:, Stephen Hawking, Bantam Books, 1988.
3142:
3076:
2992:also have an entropy and temperature.
2142:. Further considerations were made by
6557:God, the Universe and Everything Else
6211:
5762:
4789:
4282:Foster, Brendan Z. (September 2019).
3747:
3745:
2980:
2841:(Hawking radiation) at a temperature
2437:, a non-decreasing function of time:
1780:showed that black holes emit thermal
6597:Brave New World with Stephen Hawking
6298:Penrose–Hawking singularity theorems
5743:
4716:
4190:
4058:
4001:
3952:
3872:
2800:is the sum of the ordinary entropy.
1694:, leading to the formulation of the
6434:George's Secret Key to the Universe
6237:
5788:
4260:Dougherty, John; Callender, Craig.
4193:"The thermodynamics of black holes"
3875:"The Thermodynamics of Black Holes"
3389:New Frontiers in Fields and Strings
2780:is the entropy of a black hole and
2641:
2533:The zeroth law is analogous to the
2528:
2004:. This is often referred to as the
13:
6407:Brief Answers to the Big Questions
6288:Gibbons–Hawking–York boundary term
4597:"Particle creation by black holes"
3742:
3380:
3309:"Particle creation by black holes"
2803:
2572:
2433:The horizon area is, assuming the
2384:
2336:
2235:
2222:
1914:is the area of the event horizon,
854:
807:
722:
675:
587:
540:
360:Intensive and extensive properties
14:
6698:
6196:Template:Quantum mechanics topics
4764:
4360:For an authoritative review, see
2428:
2161:
1970:
6399:The Dreams That Stuff Is Made Of
6268:Chronology protection conjecture
6191:
6190:
5912:Topological quantum field theory
5742:
5733:
5732:
5031:Tolman–Oppenheimer–Volkoff limit
4902:
2489:
2173:
2114:The laws of black hole mechanics
1616:
1615:
935:Table of thermodynamic equations
27:merging, a process in which the
6458:George and the Unbreakable Code
5897:Jackiw–Teitelboim gravity
5148:Innermost stable circular orbit
4815:
4781:Black hole entropy on arxiv.org
4473:
4408:
4354:
4275:
4184:
4109:
4052:
3995:
3796:
3683:
3495:
3046:
2973:to thermodynamic systems: they
1710:requires that black holes have
1411:Maxwell's thermodynamic surface
6656:Black hole information paradox
6102:Causal dynamical triangulation
5970:Black hole information paradox
5574:Timeline of black hole physics
4059:Wald, Robert M. (1997-11-15).
3835:10.1088/0264-9381/25/23/235018
3347:
3300:
3288:
3270:
3251:
3226:
3191:
3070:
1145:
1133:
1090:
1078:
1035:
1023:
995:
983:
1:
6442:George's Cosmic Treasure Hunt
6068:Wheeler–DeWitt equation
5342:Nonsingular black hole models
4394:10.1016/S0370-1573(99)00083-6
4008:Classical and Quantum Gravity
4002:Wald, Robert M (1999-12-01).
3959:Classical and Quantum Gravity
3805:Classical and Quantum Gravity
3473:10.1103/PhysRevLett.99.201101
2743:{\displaystyle S_{BH}-S>0}
2678:quantum-statistical mechanics
2170:for a stationary black hole.
2122:are physical properties that
1728:In 1973 Bekenstein suggested
1312:Mechanical equivalent of heat
23:An artist's depiction of two
6351:The Nature of Space and Time
5990:Cosmic censorship hypothesis
5809:Batalin–Vilkovisky formalism
4703:10.1016/0550-3213(85)90418-3
4595:Hawking, Stephen W. (1975).
4197:Living Reviews in Relativity
4038:10.1088/0264-9381/16/12A/309
3879:Living Reviews in Relativity
3534:10.1016/0370-2693(96)00345-0
3258:Matson, John (Oct 1, 2010).
3063:
2680:, because the GSL is both a
2648:second law of thermodynamics
2535:zeroth law of thermodynamics
2120:laws of black hole mechanics
1934:{\displaystyle k_{\text{B}}}
1708:second law of thermodynamics
924:Onsager reciprocal relations
7:
6661:Thorne–Hawking–Preskill bet
5564:Rossi X-ray Timing Explorer
5529:Hypercompact stellar system
5519:Gamma-ray burst progenitors
4674:'t Hooft, Gerardus (1985).
4340:10.1016/j.shpsb.2018.05.002
3981:10.1088/0264-9381/17/20/410
3953:Rácz, István (2000-10-21).
3587:10.1103/PhysRevLett.77.3288
3022:
2990:cosmological event horizons
2959:
2606:first law of thermodynamics
1701:
1416:Entropy as energy dispersal
1227:"Perpetual motion" machines
1166:{\displaystyle G(T,p)=H-TS}
1111:{\displaystyle A(T,V)=U-TS}
1056:{\displaystyle H(S,p)=U+pV}
10:
6703:
6687:Branches of thermodynamics
6565:Stephen Hawking's Universe
6367:On the Shoulders of Giants
6359:The Universe in a Nutshell
6086:Hartle–Hawking state
5985:Bousso's holographic bound
5965:Black hole complementarity
5250:Black hole complementarity
5217:Bousso's holographic bound
5202:Quasi-periodic oscillation
4900:
4894:Malament–Hogarth spacetime
4642:Cambridge University Press
3648:10.1103/PhysRevLett.80.904
3407:10.1142/9789813149441_0005
2835:quantum-mechanical effects
2824:Interpretation of the laws
2650:states that the change in
2006:Bekenstein–Hawking formula
863:{\displaystyle \partial T}
816:{\displaystyle \partial V}
731:{\displaystyle \partial p}
684:{\displaystyle \partial V}
596:{\displaystyle \partial T}
549:{\displaystyle \partial S}
6638:
6615:
6605:Genius by Stephen Hawking
6548:
6505:
6482:
6425:
6375:A Briefer History of Time
6318:
6311:
6258:Black hole thermodynamics
6245:
6182:
6149:
6094:
6078:Euclidean quantum gravity
6076:
6055:Canonical quantum gravity
6053:
6020:
6013:
6005:Gravitational singularity
5975:Black-hole thermodynamics
5955:
5920:
5877:
5859:Ryu–Takayanagi conjecture
5796:
5728:
5602:
5454:
5416:
5395:
5334:
5293:
5242:
5121:Gravitational singularity
5108:
5001:
4911:
4836:
4823:
4776:Black Hole Thermodynamics
4749:10.1088/1367-2630/7/1/203
3177:10.1103/RevModPhys.74.825
3146:Reviews of Modern Physics
3119:10.1142/S0218271814300237
2513:{\displaystyle \kappa =0}
2166:The horizon has constant
2081:near-extremal black holes
2067:, using methods based on
1665:black hole thermodynamics
1337:An Inquiry Concerning the
6538:The Theory of Everything
6466:George and the Blue Moon
6418:(2023, posthume message)
6383:God Created the Integers
6132:Superfluid vacuum theory
5887:2+1D topological gravity
5705:PSO J030947.49+271757.31
5630:SDSS J150243.09+111557.3
5163:Blandford–Znajek process
4447:10.1103/PhysRevE.53.3738
4269:philsci-archive.pitt.edu
4095:10.1103/PhysRevD.56.6467
3873:Wald, Robert M. (2001).
3200:Lettere al Nuovo Cimento
3039:
2085:Schwarzschild black hole
1350:Heterogeneous Substances
767:{\displaystyle \alpha =}
635:{\displaystyle \beta =-}
6514:A Brief History of Time
6450:George and the Big Bang
6335:A Brief History of Time
6122:Noncommutative geometry
5869:Weinberg–Witten theorem
5864:Trans-Planckian problem
4961:Active galactic nucleus
4543:10.1103/PhysRevD.7.2333
3774:10.1103/physrevd.9.3292
3618:Physical Review Letters
3557:Physical Review Letters
3443:Physical Review Letters
3295:A Brief History of Time
3282:March 29, 2013, at the
2562:{\displaystyle \kappa }
2399:electrostatic potential
2342:{\displaystyle \Omega }
2298:{\displaystyle \kappa }
1678:. As the study of the
6473:Unlocking the Universe
6278:Gibbons–Hawking effect
6273:Gibbons–Hawking ansatz
5804:AdS/CFT correspondence
5589:Tidal disruption event
5559:Supermassive dark star
5477:Black holes in fiction
5462:Outline of black holes
5095:Supermassive dark star
5014:Gravitational collapse
4719:New Journal of Physics
3307:Hawking, S. W (1975).
3010:AdS/CFT correspondence
2939:
2886:
2794:
2774:
2773:{\displaystyle S_{BH}}
2744:
2702:
2632:
2594:
2563:
2524:Discussion of the laws
2514:
2477:
2415:
2391:
2367:
2343:
2323:
2299:
2275:
2252:
2038:Ryu–Takayanagi formula
2022:
1994:
1935:
1908:
1885:
1810:
1770:
1671:with the existence of
1669:laws of thermodynamics
1167:
1112:
1057:
1002:
1001:{\displaystyle U(S,V)}
864:
840:
817:
793:
768:
732:
708:
685:
661:
636:
597:
573:
550:
526:
501:
480:Specific heat capacity
84:Quantum thermodynamics
32:
29:laws of thermodynamics
6415:On the Origin of Time
6283:Gibbons–Hawking space
6030:Bosonic string theory
5942:Semiclassical gravity
5839:Holographic principle
5829:Gravitational anomaly
5467:Black Hole Initiative
5280:Holographic principle
4191:Wald, Robert (2001).
4122:Nature Communications
3005:holographic principle
2940:
2887:
2795:
2775:
2745:
2703:
2633:
2595:
2564:
2515:
2478:
2435:weak energy condition
2416:
2392:
2390:{\displaystyle \Phi }
2368:
2344:
2329:is the horizon area,
2324:
2300:
2276:
2253:
2150:Statement of the laws
2130:, were discovered by
2045:statistical mechanics
2034:holographic principle
2023:
1995:
1936:
1909:
1886:
1811:
1771:
1696:holographic principle
1680:statistical mechanics
1348:On the Equilibrium of
1168:
1113:
1066:Helmholtz free energy
1058:
1003:
865:
841:
818:
794:
769:
733:
709:
686:
662:
637:
598:
574:
551:
527:
502:
22:
6293:Hartle–Hawking state
6063:Loop quantum gravity
5922:Quantum field theory
5270:Final parsec problem
5229:Schwarzschild radius
3690:Casadio, R. (2011).
3391:. pp. 297–351.
2995:More fundamentally,
2906:
2848:
2810:extremal black holes
2784:
2754:
2712:
2692:
2616:
2581:
2553:
2520:cannot be achieved.
2498:
2444:
2405:
2381:
2357:
2333:
2313:
2289:
2265:
2185:
2108:loop quantum gravity
2092:loop quantum gravity
2012:
1949:
1918:
1898:
1823:
1792:
1732:
1684:black-body radiation
1361:Motive Power of Fire
1127:
1072:
1017:
977:
929:Bridgman's equations
906:Fundamental relation
851:
830:
804:
783:
755:
719:
698:
672:
651:
620:
584:
563:
537:
516:
488:
5932:Bunch–Davies vacuum
5924:in curved spacetime
5824:Faddeev–Popov ghost
5569:Superluminal motion
5544:Population III star
5514:Gravitational waves
5472:Black hole starship
5255:Information paradox
4741:2005NJPh....7..203P
4695:1985NuPhB.256..727T
4613:1975CMaPh..43..199H
4572:1974Natur.248...30H
4535:1973PhRvD...7.2333B
4498:1973CMaPh..31..161B
4439:1996PhRvE..53.3738C
4386:2000PhR...323..183A
4332:2018SHPMP..64...52W
4228:10.12942/lrr-2001-6
4219:2001LRR.....4....6W
4152:10.1038/ncomms14538
4144:2017NatCo...814538M
4087:1997PhRvD..56.6467W
4030:1999CQGra..16A.177W
3910:10.12942/lrr-2001-6
3901:2001LRR.....4....6W
3827:2008CQGra..25w5018W
3766:1974PhRvD...9.3292B
3718:2011Entrp..13..502C
3640:1998PhRvL..80..904A
3579:1996PhRvL..77.3288R
3526:1996PhLB..379...99S
3465:2007PhRvL..99t1101B
3374:1999InJPB..73..147M
3325:1975CMaPh..43..199H
3169:2002RvMP...74..825B
3101:2014IJMPD..2330023C
3085:(11): 1430023–736.
2631:{\displaystyle TdS}
2610:energy conservation
2604:. Analogously, the
2539:thermal equilibrium
1874:
1809:{\displaystyle 1/4}
1339:Source ... Friction
1271:Loschmidt's paradox
463:Material properties
341:Conjugate variables
6646:In popular culture
6623:Jane Wilde Hawking
6576:(2008 documentary)
6568:(1997 documentary)
6117:Group field theory
6045:Superstring theory
6000:Firewall (physics)
5403:Optical black hole
5316:Reissner–Nordström
5275:Firewall (physics)
5180:Gravitational lens
4621:10.1007/BF02345020
4506:10.1007/BF01645742
4288:quantamagazine.org
4014:(12A): A177–A190.
3358:. 73.21 (2): 147.
3333:10.1007/BF02345020
3238:2012-03-01 at the
3212:10.1007/BF02757029
2981:Beyond black holes
2950:general relativity
2935:
2882:
2790:
2770:
2740:
2698:
2628:
2608:is a statement of
2593:{\displaystyle dE}
2590:
2559:
2510:
2473:
2411:
2387:
2363:
2339:
2319:
2295:
2271:
2248:
2018:
1990:
1943:Boltzmann constant
1931:
1904:
1881:
1860:
1806:
1766:
1603:Order and disorder
1359:Reflections on the
1266:Heat death paradox
1163:
1108:
1053:
998:
860:
836:
813:
789:
764:
728:
704:
681:
657:
632:
593:
569:
546:
522:
500:{\displaystyle c=}
497:
470:Property databases
446:Reduced properties
430:Chemical potential
394:Functions of state
317:Thermal efficiency
53:Carnot heat engine
33:
6669:
6668:
6581:Genius of Britain
6501:
6500:
6253:Hawking radiation
6205:
6204:
6162:Eternal inflation
6157:Quantum cosmology
6145:
6144:
5937:Hawking radiation
5902:Liouville gravity
5756:
5755:
5549:Supermassive star
5539:Naked singularity
5534:Membrane paradigm
5260:Cosmic censorship
5234:Spaghettification
5222:Immirzi parameter
5175:Hawking radiation
5116:Astrophysical jet
5085:Supermassive star
5075:Binary black hole
5009:Stellar evolution
4951:Intermediate-mass
4683:Nuclear Physics B
4651:978-0-521-09906-6
4523:Physical Review D
4417:Physical Review E
4071:(10): 6467–6474.
4065:Physical Review D
3965:(20): 4353–4356.
3760:(12): 3292–3300.
3754:Physical Review D
3727:10.3390/e13020502
3563:(16): 3288–3291.
3504:Physics Letters B
3416:978-981-314-943-4
3245:Technology Review
3029:Joseph Polchinski
2930:
2916:
2897:geometrized units
2877:
2858:
2839:thermal radiation
2793:{\displaystyle S}
2701:{\displaystyle N}
2465:
2414:{\displaystyle Q}
2366:{\displaystyle J}
2322:{\displaystyle A}
2274:{\displaystyle E}
2210:
2156:geometrized units
2104:dynamical horizon
2100:Unruh temperature
2053:Andrew Strominger
2021:{\displaystyle A}
1988:
1959:
1928:
1907:{\displaystyle A}
1876:
1867:
1849:
1833:
1782:Hawking radiation
1758:
1688:quantum mechanics
1657:
1656:
1598:Self-organization
1423:
1422:
1121:Gibbs free energy
919:Maxwell relations
877:
876:
873:
872:
839:{\displaystyle V}
792:{\displaystyle 1}
747:Thermal expansion
741:
740:
707:{\displaystyle V}
660:{\displaystyle 1}
606:
605:
572:{\displaystyle N}
525:{\displaystyle T}
453:
452:
369:Process functions
355:Property diagrams
334:System properties
324:
323:
289:Endoreversibility
181:Equation of state
6694:
6491:My Brief History
6391:The Grand Design
6316:
6315:
6263:Micro black hole
6232:
6225:
6218:
6209:
6208:
6194:
6193:
6018:
6017:
5980:Bekenstein bound
5797:Central concepts
5783:
5776:
5769:
5760:
5759:
5746:
5745:
5736:
5735:
5408:Sonic black hole
5357:Dark-energy star
5212:Bekenstein bound
5197:M–sigma relation
5126:Ring singularity
4906:
4810:
4803:
4796:
4787:
4786:
4760:
4734:
4713:
4711:
4705:. Archived from
4680:
4670:
4668:
4655:
4632:
4591:
4580:10.1038/248030a0
4554:
4529:(8): 2333–2346.
4517:
4467:
4466:
4432:
4430:cond-mat/9601111
4423:(4): 3738–3744.
4412:
4406:
4405:
4379:
4370:(3–4): 183–386.
4358:
4352:
4351:
4325:
4305:
4299:
4298:
4296:
4294:
4279:
4273:
4272:
4266:
4257:
4251:
4250:
4240:
4230:
4212:
4188:
4182:
4181:
4171:
4137:
4113:
4107:
4106:
4080:
4056:
4050:
4049:
4023:
3999:
3993:
3992:
3974:
3950:
3941:
3940:
3930:
3912:
3894:
3870:
3861:
3860:
3854:
3846:
3820:
3800:
3794:
3793:
3749:
3740:
3739:
3729:
3711:
3687:
3681:
3680:
3678:
3666:
3660:
3659:
3633:
3613:
3607:
3606:
3572:
3552:
3546:
3545:
3519:
3499:
3493:
3492:
3458:
3438:
3429:
3428:
3400:
3384:
3378:
3377:
3367:
3351:
3345:
3344:
3304:
3298:
3292:
3286:
3274:
3268:
3267:
3255:
3249:
3230:
3224:
3223:
3195:
3189:
3188:
3162:
3140:
3131:
3130:
3112:
3094:
3074:
3057:
3050:
3001:Leonard Susskind
2944:
2942:
2941:
2936:
2931:
2923:
2918:
2917:
2914:
2891:
2889:
2888:
2883:
2878:
2876:
2865:
2860:
2859:
2856:
2799:
2797:
2796:
2791:
2779:
2777:
2776:
2771:
2769:
2768:
2749:
2747:
2746:
2741:
2727:
2726:
2707:
2705:
2704:
2699:
2670:Lovelock gravity
2666:Einstein gravity
2637:
2635:
2634:
2629:
2602:electromagnetism
2599:
2597:
2596:
2591:
2568:
2566:
2565:
2560:
2519:
2517:
2516:
2511:
2482:
2480:
2479:
2474:
2466:
2464:
2456:
2448:
2420:
2418:
2417:
2412:
2396:
2394:
2393:
2388:
2375:angular momentum
2372:
2370:
2369:
2364:
2351:angular velocity
2348:
2346:
2345:
2340:
2328:
2326:
2325:
2320:
2304:
2302:
2301:
2296:
2280:
2278:
2277:
2272:
2257:
2255:
2254:
2249:
2211:
2209:
2198:
2132:Jacob Bekenstein
2030:Bekenstein bound
2027:
2025:
2024:
2019:
1999:
1997:
1996:
1991:
1989:
1987:
1986:
1977:
1966:
1961:
1960:
1957:
1940:
1938:
1937:
1932:
1930:
1929:
1926:
1913:
1911:
1910:
1905:
1890:
1888:
1887:
1882:
1877:
1875:
1873:
1868:
1865:
1855:
1851:
1850:
1847:
1840:
1835:
1834:
1831:
1815:
1813:
1812:
1807:
1802:
1775:
1773:
1772:
1767:
1759:
1757:
1749:
1748:
1736:
1723:no-hair theorems
1719:Jacob Bekenstein
1649:
1642:
1635:
1619:
1618:
1326:Key publications
1307:
1306:("living force")
1256:Brownian ratchet
1251:Entropy and life
1246:Entropy and time
1197:
1196:
1172:
1170:
1169:
1164:
1117:
1115:
1114:
1109:
1062:
1060:
1059:
1054:
1007:
1005:
1004:
999:
901:Clausius theorem
896:Carnot's theorem
869:
867:
866:
861:
845:
843:
842:
837:
822:
820:
819:
814:
798:
796:
795:
790:
777:
776:
773:
771:
770:
765:
737:
735:
734:
729:
713:
711:
710:
705:
690:
688:
687:
682:
666:
664:
663:
658:
645:
644:
641:
639:
638:
633:
602:
600:
599:
594:
578:
576:
575:
570:
555:
553:
552:
547:
531:
529:
528:
523:
510:
509:
506:
504:
503:
498:
476:
475:
349:
348:
168:
167:
49:
35:
34:
6702:
6701:
6697:
6696:
6695:
6693:
6692:
6691:
6672:
6671:
6670:
6665:
6634:
6611:
6544:
6497:
6478:
6421:
6307:
6241:
6239:Stephen Hawking
6236:
6206:
6201:
6200:
6178:
6167:FRW/CFT duality
6141:
6090:
6072:
6049:
6009:
5951:
5923:
5916:
5873:
5792:
5790:Quantum gravity
5787:
5757:
5752:
5724:
5700:ULAS J1342+0928
5660:SDSS J0849+1114
5645:Phoenix Cluster
5598:
5450:
5412:
5391:
5330:
5289:
5285:No-hair theorem
5238:
5192:Bondi accretion
5158:Penrose process
5104:
5070:Gamma-ray burst
4997:
4907:
4898:
4884:Direct collapse
4832:
4819:
4814:
4767:
4709:
4678:
4652:
4566:(5443): 30–31.
4476:
4471:
4470:
4413:
4409:
4364:Physics Reports
4359:
4355:
4306:
4302:
4292:
4290:
4280:
4276:
4264:
4258:
4254:
4189:
4185:
4114:
4110:
4057:
4053:
4000:
3996:
3951:
3944:
3871:
3864:
3848:
3847:
3801:
3797:
3750:
3743:
3688:
3684:
3667:
3663:
3614:
3610:
3553:
3549:
3510:(1–4): 99–104.
3500:
3496:
3439:
3432:
3417:
3385:
3381:
3352:
3348:
3305:
3301:
3293:
3289:
3284:Wayback Machine
3275:
3271:
3256:
3252:
3240:Wayback Machine
3231:
3227:
3196:
3192:
3141:
3134:
3110:10.1.1.742.9918
3075:
3071:
3066:
3061:
3060:
3051:
3047:
3042:
3025:
3017:surface tension
2997:Gerard 't Hooft
2983:
2962:
2922:
2913:
2909:
2907:
2904:
2903:
2869:
2864:
2855:
2851:
2849:
2846:
2845:
2831:no-hair theorem
2826:
2806:
2785:
2782:
2781:
2761:
2757:
2755:
2752:
2751:
2719:
2715:
2713:
2710:
2709:
2693:
2690:
2689:
2686:statistical law
2644:
2617:
2614:
2613:
2582:
2579:
2578:
2577:The left side,
2575:
2554:
2551:
2550:
2531:
2526:
2499:
2496:
2495:
2492:
2457:
2449:
2447:
2445:
2442:
2441:
2431:
2423:electric charge
2406:
2403:
2402:
2382:
2379:
2378:
2358:
2355:
2354:
2334:
2331:
2330:
2314:
2311:
2310:
2307:surface gravity
2290:
2287:
2286:
2266:
2263:
2262:
2202:
2197:
2186:
2183:
2182:
2176:
2168:surface gravity
2164:
2152:
2144:Stephen Hawking
2116:
2013:
2010:
2009:
1982:
1978:
1973:
1965:
1956:
1952:
1950:
1947:
1946:
1925:
1921:
1919:
1916:
1915:
1899:
1896:
1895:
1869:
1864:
1856:
1846:
1842:
1841:
1839:
1830:
1826:
1824:
1821:
1820:
1798:
1793:
1790:
1789:
1778:Stephen Hawking
1750:
1744:
1737:
1735:
1733:
1730:
1729:
1704:
1692:quantum gravity
1653:
1608:
1607:
1583:
1575:
1574:
1573:
1433:
1425:
1424:
1403:
1389:
1364:
1360:
1353:
1349:
1342:
1338:
1305:
1298:
1280:
1261:Maxwell's demon
1223:
1194:
1193:
1177:
1176:
1175:
1128:
1125:
1124:
1123:
1073:
1070:
1069:
1068:
1018:
1015:
1014:
1013:
978:
975:
974:
973:
971:Internal energy
966:
951:
941:
940:
915:
890:
880:
879:
878:
852:
849:
848:
831:
828:
827:
805:
802:
801:
784:
781:
780:
756:
753:
752:
720:
717:
716:
699:
696:
695:
673:
670:
669:
652:
649:
648:
621:
618:
617:
612:Compressibility
585:
582:
581:
564:
561:
560:
538:
535:
534:
517:
514:
513:
489:
486:
485:
465:
455:
454:
435:Particle number
388:
347:
336:
326:
325:
284:Irreversibility
196:State of matter
163:Isolated system
148:
138:
137:
136:
111:
101:
100:
96:Non-equilibrium
88:
63:
55:
17:
12:
11:
5:
6700:
6690:
6689:
6684:
6667:
6666:
6664:
6663:
6658:
6653:
6648:
6642:
6640:
6636:
6635:
6633:
6632:
6626:
6619:
6617:
6613:
6612:
6610:
6609:
6601:
6593:
6585:
6577:
6569:
6561:
6552:
6550:
6546:
6545:
6543:
6542:
6534:
6526:
6518:
6509:
6507:
6503:
6502:
6499:
6498:
6496:
6495:
6486:
6484:
6480:
6479:
6477:
6476:
6470:
6462:
6454:
6446:
6438:
6429:
6427:
6423:
6422:
6420:
6419:
6411:
6403:
6395:
6387:
6379:
6371:
6363:
6355:
6347:
6339:
6331:
6322:
6320:
6313:
6309:
6308:
6306:
6305:
6303:Hawking energy
6300:
6295:
6290:
6285:
6280:
6275:
6270:
6265:
6260:
6255:
6249:
6247:
6243:
6242:
6235:
6234:
6227:
6220:
6212:
6203:
6202:
6199:
6198:
6184:
6183:
6180:
6179:
6177:
6176:
6175:
6174:
6169:
6164:
6153:
6151:
6147:
6146:
6143:
6142:
6140:
6139:
6137:Twistor theory
6134:
6129:
6124:
6119:
6114:
6109:
6104:
6098:
6096:
6092:
6091:
6089:
6088:
6082:
6080:
6074:
6073:
6071:
6070:
6065:
6059:
6057:
6051:
6050:
6048:
6047:
6042:
6037:
6032:
6026:
6024:
6015:
6011:
6010:
6008:
6007:
6002:
5997:
5992:
5987:
5982:
5977:
5972:
5967:
5961:
5959:
5953:
5952:
5950:
5949:
5944:
5939:
5934:
5928:
5926:
5918:
5917:
5915:
5914:
5909:
5904:
5899:
5894:
5889:
5883:
5881:
5875:
5874:
5872:
5871:
5866:
5861:
5856:
5851:
5846:
5841:
5836:
5831:
5826:
5821:
5816:
5811:
5806:
5800:
5798:
5794:
5793:
5786:
5785:
5778:
5771:
5763:
5754:
5753:
5751:
5750:
5740:
5729:
5726:
5725:
5723:
5722:
5720:Swift J1644+57
5717:
5712:
5707:
5702:
5697:
5692:
5687:
5682:
5677:
5672:
5670:MS 0735.6+7421
5667:
5662:
5657:
5652:
5647:
5642:
5637:
5635:Sagittarius A*
5632:
5627:
5622:
5617:
5612:
5606:
5604:
5600:
5599:
5597:
5596:
5591:
5586:
5581:
5576:
5571:
5566:
5561:
5556:
5551:
5546:
5541:
5536:
5531:
5526:
5521:
5516:
5511:
5510:
5509:
5504:
5494:
5489:
5484:
5479:
5474:
5469:
5464:
5458:
5456:
5452:
5451:
5449:
5448:
5443:
5438:
5433:
5428:
5422:
5420:
5414:
5413:
5411:
5410:
5405:
5399:
5397:
5393:
5392:
5390:
5389:
5384:
5379:
5374:
5369:
5364:
5359:
5354:
5349:
5344:
5338:
5336:
5332:
5331:
5329:
5328:
5323:
5318:
5313:
5308:
5297:
5295:
5291:
5290:
5288:
5287:
5282:
5277:
5272:
5267:
5262:
5257:
5252:
5246:
5244:
5240:
5239:
5237:
5236:
5231:
5226:
5225:
5224:
5214:
5209:
5207:Thermodynamics
5204:
5199:
5194:
5189:
5188:
5187:
5177:
5172:
5170:Accretion disk
5167:
5166:
5165:
5160:
5150:
5145:
5140:
5135:
5134:
5133:
5128:
5118:
5112:
5110:
5106:
5105:
5103:
5102:
5097:
5092:
5087:
5082:
5077:
5072:
5067:
5066:
5065:
5060:
5055:
5045:
5044:
5043:
5033:
5028:
5027:
5026:
5016:
5011:
5005:
5003:
4999:
4998:
4996:
4995:
4994:
4993:
4988:
4983:
4978:
4973:
4968:
4963:
4953:
4948:
4947:
4946:
4936:
4935:
4934:
4931:
4926:
4915:
4913:
4909:
4908:
4901:
4899:
4897:
4896:
4891:
4886:
4881:
4876:
4871:
4866:
4861:
4856:
4851:
4846:
4844:BTZ black hole
4840:
4838:
4834:
4833:
4831:
4830:
4824:
4821:
4820:
4813:
4812:
4805:
4798:
4790:
4784:
4783:
4778:
4773:
4766:
4765:External links
4763:
4762:
4761:
4732:hep-th/0409024
4714:
4712:on 2011-09-26.
4671:
4666:hep-th/9409195
4656:
4650:
4633:
4607:(3): 199–220.
4592:
4555:
4518:
4492:(2): 161–170.
4475:
4472:
4469:
4468:
4407:
4377:hep-th/9905111
4353:
4300:
4274:
4252:
4183:
4108:
4051:
3994:
3942:
3862:
3811:(23): 235018.
3795:
3741:
3702:(2): 502–517.
3682:
3661:
3624:(5): 904–907.
3608:
3547:
3517:hep-th/9601029
3494:
3449:(20): 201101.
3430:
3415:
3379:
3356:Indian J. Phys
3346:
3319:(3): 199–220.
3299:
3287:
3269:
3250:
3225:
3206:(15): 99–104.
3190:
3160:hep-th/0203101
3153:(3): 825–874.
3132:
3068:
3067:
3065:
3062:
3059:
3058:
3044:
3043:
3041:
3038:
3037:
3036:
3031:
3024:
3021:
2982:
2979:
2961:
2958:
2946:
2945:
2934:
2929:
2926:
2921:
2912:
2893:
2892:
2881:
2875:
2872:
2868:
2863:
2854:
2825:
2822:
2814:Nernst theorem
2805:
2802:
2789:
2767:
2764:
2760:
2739:
2736:
2733:
2730:
2725:
2722:
2718:
2697:
2643:
2642:The second law
2640:
2627:
2624:
2621:
2589:
2586:
2574:
2571:
2558:
2530:
2529:The zeroth law
2527:
2525:
2522:
2509:
2506:
2503:
2491:
2488:
2484:
2483:
2472:
2469:
2463:
2460:
2455:
2452:
2430:
2429:The second law
2427:
2410:
2386:
2362:
2338:
2318:
2294:
2270:
2259:
2258:
2247:
2244:
2241:
2237:
2234:
2231:
2228:
2224:
2221:
2218:
2215:
2208:
2205:
2201:
2196:
2193:
2190:
2175:
2172:
2163:
2162:The zeroth law
2160:
2151:
2148:
2136:Brandon Carter
2128:thermodynamics
2115:
2112:
2073:string duality
2063:black hole in
2061:supersymmetric
2017:
1985:
1981:
1976:
1972:
1969:
1964:
1955:
1924:
1903:
1892:
1891:
1880:
1872:
1863:
1859:
1854:
1845:
1838:
1829:
1805:
1801:
1797:
1765:
1762:
1756:
1753:
1747:
1743:
1740:
1703:
1700:
1676:event horizons
1655:
1654:
1652:
1651:
1644:
1637:
1629:
1626:
1625:
1624:
1623:
1610:
1609:
1606:
1605:
1600:
1595:
1590:
1584:
1581:
1580:
1577:
1576:
1572:
1571:
1566:
1561:
1556:
1551:
1546:
1541:
1536:
1531:
1526:
1521:
1516:
1511:
1506:
1501:
1496:
1491:
1486:
1481:
1476:
1471:
1466:
1461:
1456:
1451:
1446:
1441:
1435:
1434:
1431:
1430:
1427:
1426:
1421:
1420:
1419:
1418:
1413:
1405:
1404:
1402:
1401:
1398:
1394:
1391:
1390:
1388:
1387:
1382:
1380:Thermodynamics
1376:
1373:
1372:
1368:
1367:
1366:
1365:
1356:
1354:
1345:
1343:
1334:
1329:
1328:
1322:
1321:
1320:
1319:
1314:
1309:
1297:
1296:
1294:Caloric theory
1290:
1287:
1286:
1282:
1281:
1279:
1278:
1273:
1268:
1263:
1258:
1253:
1248:
1242:
1239:
1238:
1232:
1231:
1230:
1229:
1222:
1221:
1216:
1211:
1205:
1202:
1201:
1195:
1192:
1191:
1188:
1184:
1183:
1182:
1179:
1178:
1174:
1173:
1162:
1159:
1156:
1153:
1150:
1147:
1144:
1141:
1138:
1135:
1132:
1118:
1107:
1104:
1101:
1098:
1095:
1092:
1089:
1086:
1083:
1080:
1077:
1063:
1052:
1049:
1046:
1043:
1040:
1037:
1034:
1031:
1028:
1025:
1022:
1008:
997:
994:
991:
988:
985:
982:
967:
965:
964:
959:
953:
952:
947:
946:
943:
942:
939:
938:
931:
926:
921:
914:
913:
908:
903:
898:
892:
891:
886:
885:
882:
881:
875:
874:
871:
870:
859:
856:
846:
835:
824:
823:
812:
809:
799:
788:
774:
763:
760:
750:
743:
742:
739:
738:
727:
724:
714:
703:
692:
691:
680:
677:
667:
656:
642:
631:
628:
625:
615:
608:
607:
604:
603:
592:
589:
579:
568:
557:
556:
545:
542:
532:
521:
507:
496:
493:
483:
474:
473:
472:
466:
461:
460:
457:
456:
451:
450:
449:
448:
443:
438:
427:
416:
397:
396:
390:
389:
387:
386:
381:
375:
372:
371:
365:
364:
363:
362:
357:
338:
337:
332:
331:
328:
327:
322:
321:
320:
319:
314:
309:
301:
300:
294:
293:
292:
291:
286:
281:
276:
274:Free expansion
271:
266:
261:
256:
251:
246:
241:
236:
228:
227:
221:
220:
219:
218:
213:
211:Control volume
208:
203:
201:Phase (matter)
198:
193:
188:
183:
175:
174:
166:
165:
160:
155:
149:
144:
143:
140:
139:
135:
134:
129:
124:
119:
113:
112:
107:
106:
103:
102:
99:
98:
87:
86:
81:
76:
71:
65:
64:
61:
60:
57:
56:
51:The classical
50:
42:
41:
39:Thermodynamics
15:
9:
6:
4:
3:
2:
6699:
6688:
6685:
6683:
6680:
6679:
6677:
6662:
6659:
6657:
6654:
6652:
6649:
6647:
6644:
6643:
6641:
6637:
6630:
6627:
6624:
6621:
6620:
6618:
6614:
6608:(2016 series)
6607:
6606:
6602:
6600:(2011 series)
6599:
6598:
6594:
6592:(2010 series)
6591:
6590:
6586:
6584:(2010 series)
6583:
6582:
6578:
6575:
6574:
6570:
6567:
6566:
6562:
6559:
6558:
6554:
6553:
6551:
6547:
6540:
6539:
6535:
6532:
6531:
6527:
6524:
6523:
6519:
6516:
6515:
6511:
6510:
6508:
6504:
6493:
6492:
6488:
6487:
6485:
6481:
6474:
6471:
6468:
6467:
6463:
6460:
6459:
6455:
6452:
6451:
6447:
6444:
6443:
6439:
6436:
6435:
6431:
6430:
6428:
6424:
6417:
6416:
6412:
6409:
6408:
6404:
6401:
6400:
6396:
6393:
6392:
6388:
6385:
6384:
6380:
6377:
6376:
6372:
6369:
6368:
6364:
6361:
6360:
6356:
6353:
6352:
6348:
6345:
6344:
6340:
6337:
6336:
6332:
6329:
6328:
6324:
6323:
6321:
6317:
6314:
6310:
6304:
6301:
6299:
6296:
6294:
6291:
6289:
6286:
6284:
6281:
6279:
6276:
6274:
6271:
6269:
6266:
6264:
6261:
6259:
6256:
6254:
6251:
6250:
6248:
6244:
6240:
6233:
6228:
6226:
6221:
6219:
6214:
6213:
6210:
6197:
6189:
6186:
6185:
6181:
6173:
6170:
6168:
6165:
6163:
6160:
6159:
6158:
6155:
6154:
6152:
6148:
6138:
6135:
6133:
6130:
6128:
6125:
6123:
6120:
6118:
6115:
6113:
6112:Dual graviton
6110:
6108:
6105:
6103:
6100:
6099:
6097:
6093:
6087:
6084:
6083:
6081:
6079:
6075:
6069:
6066:
6064:
6061:
6060:
6058:
6056:
6052:
6046:
6043:
6041:
6038:
6036:
6033:
6031:
6028:
6027:
6025:
6023:
6022:String theory
6019:
6016:
6012:
6006:
6003:
6001:
5998:
5996:
5993:
5991:
5988:
5986:
5983:
5981:
5978:
5976:
5973:
5971:
5968:
5966:
5963:
5962:
5960:
5958:
5954:
5948:
5945:
5943:
5940:
5938:
5935:
5933:
5930:
5929:
5927:
5925:
5919:
5913:
5910:
5908:
5905:
5903:
5900:
5898:
5895:
5893:
5890:
5888:
5885:
5884:
5882:
5880:
5876:
5870:
5867:
5865:
5862:
5860:
5857:
5855:
5852:
5850:
5847:
5845:
5842:
5840:
5837:
5835:
5832:
5830:
5827:
5825:
5822:
5820:
5817:
5815:
5812:
5810:
5807:
5805:
5802:
5801:
5799:
5795:
5791:
5784:
5779:
5777:
5772:
5770:
5765:
5764:
5761:
5749:
5741:
5739:
5731:
5730:
5727:
5721:
5718:
5716:
5713:
5711:
5708:
5706:
5703:
5701:
5698:
5696:
5695:Markarian 501
5693:
5691:
5688:
5686:
5683:
5681:
5678:
5676:
5673:
5671:
5668:
5666:
5663:
5661:
5658:
5656:
5653:
5651:
5648:
5646:
5643:
5641:
5638:
5636:
5633:
5631:
5628:
5626:
5623:
5621:
5620:XTE J1118+480
5618:
5616:
5615:XTE J1650-500
5613:
5611:
5608:
5607:
5605:
5601:
5595:
5592:
5590:
5587:
5585:
5582:
5580:
5577:
5575:
5572:
5570:
5567:
5565:
5562:
5560:
5557:
5555:
5552:
5550:
5547:
5545:
5542:
5540:
5537:
5535:
5532:
5530:
5527:
5525:
5522:
5520:
5517:
5515:
5512:
5508:
5505:
5503:
5500:
5499:
5498:
5495:
5493:
5490:
5488:
5485:
5483:
5480:
5478:
5475:
5473:
5470:
5468:
5465:
5463:
5460:
5459:
5457:
5453:
5447:
5444:
5442:
5439:
5437:
5434:
5432:
5429:
5427:
5424:
5423:
5421:
5419:
5415:
5409:
5406:
5404:
5401:
5400:
5398:
5394:
5388:
5385:
5383:
5380:
5378:
5375:
5373:
5370:
5368:
5365:
5363:
5360:
5358:
5355:
5353:
5350:
5348:
5345:
5343:
5340:
5339:
5337:
5333:
5327:
5324:
5322:
5319:
5317:
5314:
5312:
5309:
5306:
5302:
5301:Schwarzschild
5299:
5298:
5296:
5292:
5286:
5283:
5281:
5278:
5276:
5273:
5271:
5268:
5266:
5263:
5261:
5258:
5256:
5253:
5251:
5248:
5247:
5245:
5241:
5235:
5232:
5230:
5227:
5223:
5220:
5219:
5218:
5215:
5213:
5210:
5208:
5205:
5203:
5200:
5198:
5195:
5193:
5190:
5186:
5183:
5182:
5181:
5178:
5176:
5173:
5171:
5168:
5164:
5161:
5159:
5156:
5155:
5154:
5151:
5149:
5146:
5144:
5143:Photon sphere
5141:
5139:
5138:Event horizon
5136:
5132:
5129:
5127:
5124:
5123:
5122:
5119:
5117:
5114:
5113:
5111:
5107:
5101:
5098:
5096:
5093:
5091:
5088:
5086:
5083:
5081:
5078:
5076:
5073:
5071:
5068:
5064:
5063:Related links
5061:
5059:
5056:
5054:
5051:
5050:
5049:
5046:
5042:
5041:Related links
5039:
5038:
5037:
5034:
5032:
5029:
5025:
5024:Related links
5022:
5021:
5020:
5017:
5015:
5012:
5010:
5007:
5006:
5004:
5000:
4992:
4989:
4987:
4984:
4982:
4979:
4977:
4974:
4972:
4969:
4967:
4964:
4962:
4959:
4958:
4957:
4954:
4952:
4949:
4945:
4942:
4941:
4940:
4937:
4932:
4930:
4927:
4925:
4922:
4921:
4920:
4917:
4916:
4914:
4910:
4905:
4895:
4892:
4890:
4887:
4885:
4882:
4880:
4877:
4875:
4872:
4870:
4867:
4865:
4862:
4860:
4857:
4855:
4852:
4850:
4849:Schwarzschild
4847:
4845:
4842:
4841:
4839:
4835:
4829:
4826:
4825:
4822:
4818:
4811:
4806:
4804:
4799:
4797:
4792:
4791:
4788:
4782:
4779:
4777:
4774:
4772:
4769:
4768:
4758:
4754:
4750:
4746:
4742:
4738:
4733:
4728:
4724:
4720:
4715:
4708:
4704:
4700:
4696:
4692:
4688:
4684:
4677:
4672:
4667:
4662:
4657:
4653:
4647:
4643:
4639:
4634:
4630:
4626:
4622:
4618:
4614:
4610:
4606:
4602:
4598:
4593:
4589:
4585:
4581:
4577:
4573:
4569:
4565:
4561:
4556:
4552:
4548:
4544:
4540:
4536:
4532:
4528:
4524:
4519:
4515:
4511:
4507:
4503:
4499:
4495:
4491:
4487:
4483:
4478:
4477:
4464:
4460:
4456:
4452:
4448:
4444:
4440:
4436:
4431:
4426:
4422:
4418:
4411:
4403:
4399:
4395:
4391:
4387:
4383:
4378:
4373:
4369:
4365:
4357:
4349:
4345:
4341:
4337:
4333:
4329:
4324:
4319:
4315:
4311:
4304:
4289:
4285:
4278:
4270:
4263:
4256:
4248:
4244:
4239:
4234:
4229:
4224:
4220:
4216:
4211:
4210:gr-qc/9912119
4206:
4202:
4198:
4194:
4187:
4179:
4175:
4170:
4165:
4161:
4157:
4153:
4149:
4145:
4141:
4136:
4131:
4127:
4123:
4119:
4112:
4104:
4100:
4096:
4092:
4088:
4084:
4079:
4078:gr-qc/9704008
4074:
4070:
4066:
4062:
4055:
4047:
4043:
4039:
4035:
4031:
4027:
4022:
4021:gr-qc/9901033
4017:
4013:
4009:
4005:
3998:
3990:
3986:
3982:
3978:
3973:
3972:gr-qc/0009049
3968:
3964:
3960:
3956:
3949:
3947:
3938:
3934:
3929:
3924:
3920:
3916:
3911:
3906:
3902:
3898:
3893:
3892:gr-qc/9912119
3888:
3884:
3880:
3876:
3869:
3867:
3858:
3852:
3844:
3840:
3836:
3832:
3828:
3824:
3819:
3814:
3810:
3806:
3799:
3791:
3787:
3783:
3779:
3775:
3771:
3767:
3763:
3759:
3755:
3748:
3746:
3737:
3733:
3728:
3723:
3719:
3715:
3710:
3705:
3701:
3697:
3693:
3686:
3677:
3672:
3665:
3657:
3653:
3649:
3645:
3641:
3637:
3632:
3631:gr-qc/9710007
3627:
3623:
3619:
3612:
3604:
3600:
3596:
3592:
3588:
3584:
3580:
3576:
3571:
3570:gr-qc/9603063
3566:
3562:
3558:
3551:
3543:
3539:
3535:
3531:
3527:
3523:
3518:
3513:
3509:
3505:
3498:
3490:
3486:
3482:
3478:
3474:
3470:
3466:
3462:
3457:
3456:gr-qc/0702006
3452:
3448:
3444:
3437:
3435:
3426:
3422:
3418:
3412:
3408:
3404:
3399:
3394:
3390:
3383:
3375:
3371:
3366:
3365:gr-qc/9807045
3361:
3357:
3350:
3342:
3338:
3334:
3330:
3326:
3322:
3318:
3314:
3310:
3303:
3296:
3291:
3285:
3281:
3278:
3273:
3265:
3261:
3254:
3247:
3246:
3241:
3237:
3234:
3229:
3221:
3217:
3213:
3209:
3205:
3201:
3194:
3186:
3182:
3178:
3174:
3170:
3166:
3161:
3156:
3152:
3148:
3147:
3139:
3137:
3128:
3124:
3120:
3116:
3111:
3106:
3102:
3098:
3093:
3088:
3084:
3080:
3073:
3069:
3055:
3049:
3045:
3035:
3032:
3030:
3027:
3026:
3020:
3018:
3013:
3011:
3006:
3002:
2998:
2993:
2991:
2987:
2978:
2976:
2972:
2966:
2957:
2955:
2951:
2932:
2927:
2924:
2919:
2910:
2902:
2901:
2900:
2898:
2879:
2873:
2870:
2866:
2861:
2852:
2844:
2843:
2842:
2840:
2836:
2832:
2821:
2817:
2815:
2811:
2804:The third law
2801:
2787:
2765:
2762:
2758:
2737:
2734:
2731:
2728:
2723:
2720:
2716:
2695:
2687:
2683:
2679:
2673:
2671:
2667:
2662:
2656:
2653:
2649:
2639:
2625:
2622:
2619:
2611:
2607:
2603:
2587:
2584:
2573:The first law
2570:
2556:
2548:
2544:
2540:
2536:
2521:
2507:
2504:
2501:
2490:The third law
2487:
2470:
2467:
2461:
2458:
2453:
2450:
2440:
2439:
2438:
2436:
2426:
2424:
2408:
2400:
2376:
2360:
2352:
2316:
2308:
2292:
2284:
2268:
2245:
2242:
2239:
2232:
2229:
2226:
2219:
2216:
2213:
2206:
2203:
2199:
2194:
2191:
2188:
2181:
2180:
2179:
2174:The first law
2171:
2169:
2159:
2157:
2147:
2145:
2141:
2140:James Bardeen
2137:
2133:
2129:
2125:
2121:
2111:
2109:
2105:
2101:
2097:
2093:
2088:
2086:
2082:
2078:
2074:
2070:
2066:
2065:string theory
2062:
2058:
2054:
2050:
2046:
2041:
2039:
2035:
2031:
2015:
2007:
2003:
2002:Planck length
1983:
1979:
1974:
1967:
1962:
1953:
1944:
1922:
1901:
1878:
1870:
1861:
1857:
1852:
1843:
1836:
1827:
1819:
1818:
1817:
1803:
1799:
1795:
1787:
1786:thermodynamic
1783:
1779:
1763:
1760:
1754:
1751:
1745:
1741:
1738:
1726:
1724:
1720:
1715:
1713:
1709:
1699:
1697:
1693:
1689:
1685:
1681:
1677:
1674:
1670:
1666:
1662:
1650:
1645:
1643:
1638:
1636:
1631:
1630:
1628:
1627:
1622:
1614:
1613:
1612:
1611:
1604:
1601:
1599:
1596:
1594:
1593:Self-assembly
1591:
1589:
1586:
1585:
1579:
1578:
1570:
1567:
1565:
1564:van der Waals
1562:
1560:
1557:
1555:
1552:
1550:
1547:
1545:
1542:
1540:
1537:
1535:
1532:
1530:
1527:
1525:
1522:
1520:
1517:
1515:
1512:
1510:
1507:
1505:
1502:
1500:
1497:
1495:
1492:
1490:
1489:von Helmholtz
1487:
1485:
1482:
1480:
1477:
1475:
1472:
1470:
1467:
1465:
1462:
1460:
1457:
1455:
1452:
1450:
1447:
1445:
1442:
1440:
1437:
1436:
1429:
1428:
1417:
1414:
1412:
1409:
1408:
1407:
1406:
1399:
1396:
1395:
1393:
1392:
1386:
1383:
1381:
1378:
1377:
1375:
1374:
1370:
1369:
1363:
1362:
1355:
1352:
1351:
1344:
1341:
1340:
1333:
1332:
1331:
1330:
1327:
1324:
1323:
1318:
1315:
1313:
1310:
1308:
1304:
1300:
1299:
1295:
1292:
1291:
1289:
1288:
1284:
1283:
1277:
1274:
1272:
1269:
1267:
1264:
1262:
1259:
1257:
1254:
1252:
1249:
1247:
1244:
1243:
1241:
1240:
1237:
1234:
1233:
1228:
1225:
1224:
1220:
1217:
1215:
1212:
1210:
1207:
1206:
1204:
1203:
1199:
1198:
1189:
1186:
1185:
1181:
1180:
1160:
1157:
1154:
1151:
1148:
1142:
1139:
1136:
1130:
1122:
1119:
1105:
1102:
1099:
1096:
1093:
1087:
1084:
1081:
1075:
1067:
1064:
1050:
1047:
1044:
1041:
1038:
1032:
1029:
1026:
1020:
1012:
1009:
992:
989:
986:
980:
972:
969:
968:
963:
960:
958:
955:
954:
950:
945:
944:
937:
936:
932:
930:
927:
925:
922:
920:
917:
916:
912:
911:Ideal gas law
909:
907:
904:
902:
899:
897:
894:
893:
889:
884:
883:
857:
847:
833:
826:
825:
810:
800:
786:
779:
778:
775:
761:
758:
751:
748:
745:
744:
725:
715:
701:
694:
693:
678:
668:
654:
647:
646:
643:
629:
626:
623:
616:
613:
610:
609:
590:
580:
566:
559:
558:
543:
533:
519:
512:
511:
508:
494:
491:
484:
481:
478:
477:
471:
468:
467:
464:
459:
458:
447:
444:
442:
441:Vapor quality
439:
437:
436:
431:
428:
426:
425:
420:
417:
414:
410:
409:
404:
401:
400:
399:
398:
395:
392:
391:
385:
382:
380:
377:
376:
374:
373:
370:
367:
366:
361:
358:
356:
353:
352:
351:
350:
346:
342:
335:
330:
329:
318:
315:
313:
310:
308:
305:
304:
303:
302:
299:
296:
295:
290:
287:
285:
282:
280:
279:Reversibility
277:
275:
272:
270:
267:
265:
262:
260:
257:
255:
252:
250:
247:
245:
242:
240:
237:
235:
232:
231:
230:
229:
226:
223:
222:
217:
214:
212:
209:
207:
204:
202:
199:
197:
194:
192:
189:
187:
184:
182:
179:
178:
177:
176:
173:
170:
169:
164:
161:
159:
156:
154:
153:Closed system
151:
150:
147:
142:
141:
133:
130:
128:
125:
123:
120:
118:
115:
114:
110:
105:
104:
97:
93:
90:
89:
85:
82:
80:
77:
75:
72:
70:
67:
66:
59:
58:
54:
48:
44:
43:
40:
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36:
30:
26:
21:
16:Area of study
6629:Lucy Hawking
6625:(first wife)
6603:
6595:
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6571:
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6529:
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6357:
6349:
6341:
6333:
6325:
6257:
6187:
6150:Applications
6040:Supergravity
5974:
5947:Unruh effect
5854:Quantum foam
5849:Planck units
5844:IR/UV mixing
5819:Causal patch
5650:PKS 1302-102
5524:Gravity well
5492:Compact star
5446:Microquasars
5431:Most massive
5335:Alternatives
5206:
5100:X-ray binary
5019:Neutron star
4956:Supermassive
4933:Hawking star
4874:Supermassive
4722:
4718:
4707:the original
4686:
4682:
4640:. New York:
4637:
4604:
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4563:
4559:
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4485:
4474:Bibliography
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4291:. Retrieved
4287:
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2986:Gary Gibbons
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2829:and, by the
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1658:
1454:Carathéodory
1385:Heat engines
1357:
1346:
1335:
1317:Motive power
1302:
962:Free entropy
933:
433:
432: /
422:
421: /
413:introduction
406:
405: /
344:
307:Heat engines
94: /
6682:Black holes
6107:Causal sets
5957:Black holes
5640:Centaurus A
5594:Planet Nine
5497:Exotic star
5426:Black holes
5372:Planck star
5321:Kerr–Newman
5036:White dwarf
4986:Radio-Quiet
4944:Microquasar
4817:Black holes
4689:: 727–745.
4293:3 September
3034:Robert Wald
2543:temperature
2124:black holes
2057:Cumrun Vafa
1276:Synergetics
957:Free energy
403:Temperature
264:Quasistatic
259:Isenthalpic
216:Instruments
206:Equilibrium
158:Open system
92:Equilibrium
74:Statistical
25:black holes
6676:Categories
6631:(daughter)
6549:Television
6172:Multiverse
6014:Approaches
5892:CGHS model
5879:Toy models
5814:CA-duality
5690:Q0906+6930
5680:Hercules A
5610:Cygnus X-1
5579:White hole
5554:Quasi-star
5507:Preon star
5502:Quark star
5487:Big Bounce
5347:Black star
5305:Derivation
5153:Ergosphere
5109:Properties
5090:Quasi-star
5080:Quark star
4991:Radio-Loud
4879:Primordial
4869:Kugelblitz
4725:(1): 203.
4323:1710.02724
3398:1609.00026
2708:nucleons,
1673:black hole
1588:Nucleation
1432:Scientists
1236:Philosophy
949:Potentials
312:Heat pumps
269:Polytropic
254:Isentropic
244:Isothermal
31:are upheld
6651:Namesakes
6188:See also:
6127:Spin foam
5907:RST model
5715:AT2018hyz
5362:Gravastar
5352:Dark star
5185:Microlens
5058:Hypernova
5053:Micronova
5048:Supernova
5002:Formation
4757:119047329
4551:122636624
4402:119101855
4160:2041-1723
4135:1412.3828
4103:0556-2821
4046:0264-9381
3989:0264-9381
3919:1433-8351
3843:119117894
3818:0801.2688
3790:123043135
3782:0556-2821
3736:120254309
3709:1101.1384
3676:1204.5122
3489:119496541
3425:119273886
3242:from the
3220:120254309
3127:119114925
3105:CiteSeerX
3092:1410.1486
3064:Citations
2971:analogous
2874:π
2867:κ
2729:−
2557:κ
2502:κ
2468:≥
2385:Φ
2337:Ω
2293:κ
2236:Φ
2223:Ω
2207:π
2200:κ
2118:The four
1971:ℏ
1954:ℓ
1862:ℓ
1761:≈
1755:π
1742:
1717:In 1972,
1569:Waterston
1519:von Mayer
1474:de Donder
1464:Clapeyron
1444:Boltzmann
1439:Bernoulli
1400:Education
1371:Timelines
1155:−
1100:−
888:Equations
855:∂
808:∂
759:α
723:∂
676:∂
630:−
624:β
588:∂
541:∂
249:Adiabatic
239:Isochoric
225:Processes
186:Ideal gas
69:Classical
6035:M-theory
5995:ER = EPR
5834:Graviton
5738:Category
5625:A0620-00
5584:Wormhole
5482:Big Bang
5382:Fuzzball
5265:ER = EPR
5131:Theorems
4929:Electron
4924:Extremal
4854:Rotating
4629:55539246
4514:54690354
4348:73706680
4247:28163633
4203:(1): 6.
4178:28290452
3937:28163633
3885:(1): 6.
3656:18980849
3603:43493308
3595:10062183
3481:18233129
3341:55539246
3280:Archived
3236:Archived
3185:55096624
3023:See also
2960:Critique
2750:, where
2096:spinfoam
2077:extremal
2069:D-branes
1702:Overview
1621:Category
1559:Thompson
1469:Clausius
1449:Bridgman
1303:Vis viva
1285:Theories
1219:Gas laws
1011:Enthalpy
419:Pressure
234:Isobaric
191:Real gas
79:Chemical
62:Branches
6530:Hawking
6522:Hawking
6483:Memoirs
6426:Fiction
6319:Science
6246:Physics
5748:Commons
5710:P172+18
5665:TON 618
5603:Notable
5455:Related
5441:Quasars
5436:Nearest
5396:Analogs
5326:Hayward
5294:Metrics
4939:Stellar
4864:Virtual
4859:Charged
4828:Outline
4737:Bibcode
4691:Bibcode
4609:Bibcode
4588:4290107
4568:Bibcode
4531:Bibcode
4494:Bibcode
4463:7115890
4455:9964684
4435:Bibcode
4382:Bibcode
4328:Bibcode
4238:5253844
4215:Bibcode
4169:5355879
4140:Bibcode
4083:Bibcode
4026:Bibcode
3928:5253844
3897:Bibcode
3823:Bibcode
3762:Bibcode
3714:Bibcode
3696:Entropy
3636:Bibcode
3575:Bibcode
3542:1041890
3522:Bibcode
3461:Bibcode
3370:Bibcode
3321:Bibcode
3264:Sci. Am
3165:Bibcode
3097:Bibcode
2682:quantum
2661:entropy
2652:entropy
2421:is the
2397:is the
2373:is the
2349:is the
2305:is the
2281:is the
2049:no-hair
2000:is the
1941:is the
1712:entropy
1661:physics
1544:Smeaton
1539:Rankine
1529:Onsager
1514:Maxwell
1509:Massieu
1214:Entropy
1209:General
1200:History
1190:Culture
1187:History
411: (
408:Entropy
345:italics
146:Systems
6616:Family
6560:(1988)
6541:(2014)
6533:(2013)
6525:(2004)
6517:(1991)
6494:(2013)
6475:(2020)
6469:(2016)
6461:(2014)
6453:(2011)
6445:(2009)
6437:(2007)
6410:(2018)
6402:(2011)
6394:(2010)
6386:(2005)
6378:(2005)
6370:(2002)
6362:(2001)
6354:(1996)
6346:(1993)
6338:(1988)
6330:(1973)
6095:Others
5685:3C 273
5675:NeVe 1
5655:OJ 287
5377:Q star
5243:Issues
4976:Blazar
4966:Quasar
4755:
4648:
4627:
4586:
4560:Nature
4549:
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3125:
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2283:energy
2261:where
2138:, and
1945:, and
1894:where
1534:Planck
1524:Nernst
1499:Kelvin
1459:Carnot
749:
614:
482:
424:Volume
339:Note:
298:Cycles
127:Second
117:Zeroth
6639:Other
6506:Films
6312:Books
5418:Lists
4919:Micro
4889:Rogue
4837:Types
4753:S2CID
4727:arXiv
4710:(PDF)
4679:(PDF)
4661:arXiv
4625:S2CID
4584:S2CID
4547:S2CID
4510:S2CID
4459:S2CID
4425:arXiv
4398:S2CID
4372:arXiv
4344:S2CID
4318:arXiv
4265:(PDF)
4205:arXiv
4130:arXiv
4073:arXiv
4016:arXiv
3967:arXiv
3887:arXiv
3839:S2CID
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3786:S2CID
3732:S2CID
3704:arXiv
3671:arXiv
3652:S2CID
3626:arXiv
3599:S2CID
3565:arXiv
3538:S2CID
3512:arXiv
3485:S2CID
3451:arXiv
3421:S2CID
3393:arXiv
3360:arXiv
3337:S2CID
3216:S2CID
3181:S2CID
3155:arXiv
3123:S2CID
3087:arXiv
3040:Notes
1764:0.276
1582:Other
1549:Stahl
1504:Lewis
1494:Joule
1484:Gibbs
1479:Duhem
172:State
132:Third
122:First
5387:Geon
5311:Kerr
4912:Size
4646:ISBN
4451:PMID
4295:2021
4243:PMID
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3985:ISSN
3933:PMID
3915:ISSN
3857:link
3778:ISSN
3591:PMID
3477:PMID
3411:ISBN
3052:See
2999:and
2735:>
2684:and
2401:and
2079:and
2071:and
2055:and
1706:The
1554:Tait
384:Heat
379:Work
109:Laws
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4971:LQG
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4687:256
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