254:, Ray Kurzweil cites the calculations of Seth Lloyd that a universal-scale computer is capable of 10 operations per second. The mass of the universe can be estimated at 3 Ă— 10 kilograms. If all matter in the universe was turned into a black hole, it would have a lifetime of 2.8 Ă— 10 seconds before evaporating due to Hawking radiation. During that lifetime such a universal-scale black hole computer would perform 2.8 Ă— 10 operations.
168:, without spending more energy on cooling than is saved in computation. However, on a timescale of 10 – 10 years, the cosmic microwave background radiation will be decreasing exponentially, which has been argued to eventually enable 10 as much computations per unit of energy. Important parts of this argument have been disputed.
245:). Lloyd notes that "Interestingly, although this hypothetical computation is performed at ultra-high densities and speeds, the total number of bits available to be processed is not far from the number available to current computers operating in more familiar surroundings."
371:
Many limits derived in terms of physical constants and abstract models of computation in computer science are loose. Very few known limits directly obstruct leading-edge technologies, but many engineering obstacles currently cannot be explained by closed-form limits.
232:
calculated the computational abilities of an "ultimate laptop" formed by compressing a kilogram of matter into a black hole of radius 1.485 × 10 meters, concluding that it would only last about 10 seconds before
357:
189:
used for these purposes. Such a star would have to be artificially constructed, as no natural degenerate stars will cool to this temperature for an extremely long time. It is also possible that
279:
describes the degree to which problems are computable, whereas complexity theory describes the asymptotic degree of resource consumption. Computational problems are therefore confined into
359:
of the arithmetical hierarchy classifies computable, partial functions. Moreover, this hierarchy is strict such that at any other class in the arithmetic hierarchy classifies strictly
665:
Sandberg, Anders; Armstrong, Stuart; Cirkovic, Milan M. (2017-04-27). "That is not dead which can eternal lie: the aestivation hypothesis for resolving Fermi's paradox".
216:
as a data storage or computing device, if a practical mechanism for extraction of contained information can be found. Such extraction may in principle be possible (
241:, but that during this brief time it could compute at a rate of about 5 × 10 operations per second, ultimately performing about 10 operations on 10 bits (~1
75:
limit the data storage of a system based on its energy, number of particles and particle modes. In practice, it is a stronger bound than the
Bekenstein bound.
857:
185:
could conceivably be used as a giant data storage device, by carefully perturbing it to various excited states, in the same manner as an atom or
118:. Computational algorithms can then be designed that require arbitrarily small amounts of energy/time per one elementary computation step.
177:
Several methods have been proposed for producing computing devices or data storage devices that approach physical and practical limits:
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23:
are governed by a number of different factors. In particular, there are several physical and practical limits to the amount of
439:
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classify the degree to which problems are respectively computable and computable in polynomial time. For instance, the level
165:
197:
could form complex "molecules", which some have suggested might be used for computing purposes, creating a type of
916:
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264:
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sets a bound on the maximum computational speed per unit of energy: 6 × 10 operations per second per
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440:"The Physics of Information Processing Superobjects: Daily Life Among the Jupiter Brains"
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Sinitsyn, Nikolai A. (2018). "Is there a quantum limit on speed of computation?".
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Jordan, Stephen P. (2017). "Fast quantum computation at arbitrarily low energy".
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583:"The physics of forgetting: Landauer's erasure principle and information theory"
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Bennett, Charles H.; Hanson, Robin; Riedel, C. Jess (1 August 2019).
412:
948:
Markov, Igor (2014). "Limits on
Fundamental Limits to Computation".
704:
671:
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242:
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190:
172:
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795:
Lloyd, Seth (2000). "Ultimate physical limits to computation".
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205:, which would be faster and denser than computronium based on
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352:{\displaystyle \Sigma _{0}^{0}=\Pi _{0}^{0}=\Delta _{0}^{0}}
114:. This bound, however, can be avoided if there is access to
770:"Femtotech? (Sub)Nuclear Scale Engineering and Computation"
224:). This would achieve storage density exactly equal to the
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275:of computational problems are often sought-after.
351:
1009:
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152:is the operating temperature of the computer.
173:Building devices that approach physical limits
140:consumed per irreversible state change, where
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160:cannot, even in theory, be made lower than 3
31:that can be performed with a given amount of
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858:"Ultimate physical limits to computation"
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438:Sandberg, Anders (22 December 1999).
166:cosmic microwave background radiation
164:, the approximate temperature of the
156:is not subject to this lower bound.
16:Overview of the limits of computation
756:The Internet Encyclopedia of Science
447:Journal of Evolution and Technology
259:Abstract limits in computer science
79:
13:
581:Vitelli, M.B.; Plenio, V. (2001).
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317:
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47:Hardware limits or physical limits
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937:. New York: Viking. p. 911.
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560:10.1016/j.physleta.2017.12.042
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222:black hole information paradox
220:'s proposed resolution to the
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52:Processing and memory density
265:theoretical computer science
212:It may be possible to use a
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69:with the same surface area.
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1039:
722:10.1007/s10701-019-00289-5
507:10.1103/physreva.95.032305
418:Transcomputational problem
620:10.1080/00107510010018916
108:Margolus–Levitin theorem
935:The Singularity is Near
752:"Life on neutron stars"
251:The Singularity Is Near
933:Kurzweil, Ray (2005).
692:Foundations of Physics
398:Physics of computation
367:Loose and tight limits
353:
285:arithmetical hierarchy
1023:Theory of computation
1018:Limits of computation
354:
21:limits of computation
856:Lloyd, Seth (2000).
590:Contemporary Physics
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289:polynomial hierarchy
277:Computability theory
154:Reversible computing
129:Landauer's principle
101:Communication delays
982:10.1038/nature13570
974:2014Natur.512..147M
889:2000Natur.406.1047L
873:(6799): 1047–1054.
819:2000Natur.406.1047L
803:(6799): 1047–1054.
776:on October 25, 2004
714:2019FoPh...49..820B
612:2001ConPh..42...25P
552:2018PhLA..382..477S
499:2017PhRvA..95c2305J
403:Programmable matter
348:
330:
312:
94:quantum uncertainty
922:on August 7, 2008.
349:
334:
316:
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281:complexity classes
193:on the surface of
146:Boltzmann constant
86:Bremermann's limit
958:(7513): 147–154.
530:Physics Letters A
408:Quantum computing
239:Hawking radiation
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915:. Archived from
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393:Matrioshka brain
388:Hypercomputation
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263:In the field of
226:Bekenstein bound
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218:Stephen Hawking
203:femtotechnology
183:degenerate star
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451:the original
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361:uncomputable
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199:computronium
187:quantum well
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96:constraints.
29:data storage
20:
18:
780:October 30,
636:10044/1/435
363:functions.
235:evaporating
90:mass–energy
25:computation
1012:Categories
705:1902.06730
672:1705.03394
543:1701.05550
490:1701.01175
425:References
273:complexity
230:Seth Lloyd
214:black hole
67:black hole
965:1408.3821
738:119045181
730:1572-9516
644:0010-7514
628:1366-5812
515:118953874
413:Supertask
336:Δ
318:Π
300:Σ
201:based on
990:25119233
905:10984064
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568:55887738
376:See also
191:nucleons
998:4458968
970:Bibcode
885:Bibcode
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710:Bibcode
652:9092795
608:Bibcode
548:Bibcode
495:Bibcode
283:. The
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586:(PDF)
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112:joule
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