279:. When we talk about such macroscopic properties in thermodynamics, in certain cases, we can see irreversibility in the time evolution of these quantities on a statistical level. Indeed, the second law of thermodynamics predicates that the entropy of the entire universe must not decrease, not because the probability of that is zero, but because it is so unlikely that it is a
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260:
during the process. Note, however, that the fundamental laws that underlie the thermodynamic processes are all time-reversible (classical laws of motion and laws of electrodynamics), which means that on the microscopic level, if one were to keep track of all the particles and all the degrees of
1044:
Parvasi, Seyed
Mohammad; Ho, Siu Chun Michael; Kong, Qingzhao; Mousavi, Reza; Song, Gangbing (19 July 2016). "Real time bolt preload monitoring using piezoceramic transducers and time reversal technique—a numerical study with experimental verification".
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is a process in which this property is used to reverse a received signal; this signal is then re-emitted and a temporal compression occurs, resulting in a reversal of the initial excitation waveform being played at the initial source.
328:
709:
205:
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is symmetrical under time reversal, so the time reversal of any valid solution is also a solution. This means that a wave's path through space is valid when travelled in either direction.
85:) π which gives a one-to-one mapping between the time-reversed evolution of any one state and the forward-time evolution of another corresponding state, given by the operator equation:
137:
222:
is not invariant under T-symmetry alone; if weak interactions are present, reversible dynamics are still possible, but only if the operator π also reverses the signs of all the
564:{\displaystyle p(x_{t},x_{t+\tau _{1}},x_{t+\tau _{2}},\ldots ,x_{t+\tau _{k}})=p(x_{t'},x_{t'-\tau _{1}},x_{t'-\tau _{2}},\ldots ,x_{t'-\tau _{k}})}
61:
is reversible if the statistical properties of the process are the same as the statistical properties for time-reversed data from the same process.
301:
is time-reversible if the joint probabilities of the forward and reverse state sequences are the same for all sets of time increments {
750:
261:
freedom, the many-body system processes are all reversible; However, such analysis is beyond the capability of any human being (or
593:
150:) which the dynamics give rise to must therefore either be self-symmetrical or have symmetrical images under the involution π.
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Löpker, A.; Palmowski, Z. (2013). "On time reversal of piecewise deterministic Markov processes".
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34:
if the dynamics of the process remain well-defined when the sequence of time-states is reversed.
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since standard wave equations only contain even derivatives of the unknown variables. Thus, the
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Anderson, B. E., M. Griffa, C. Larmat, T.J. Ulrich, and P.A. Johnson, "Time reversal",
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Time reversal of numerous classes of stochastic processes has been studied, including
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can only be reversible if their stationary distributions have the property of
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exhibit time reversibility, as long as the operator π reverses the
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is time-reversible if the time-reversed process satisfies the same
1013:
761:
Time reversal method works based on the linear reciprocity of the
257:
159:
238:). This reversibility of several linked properties is known as
269:(like entropy and temperature) of many-body system are only
81:, so that for every state there exists a transformation (an
704:{\displaystyle p(x_{t}=i,x_{t+1}=j)=\,p(x_{t}=j,x_{t+1}=i)}
45:
as the original process; in other words, the equations are
1101:
https://acousticstoday.org/time-reversal-brian-e-anderson/
1117:
Isham, V. (1991) "Modelling stochastic phenomena". In:
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331:
200:{\displaystyle \mathbf {p} \rightarrow \mathbf {-p} }
180:
94:
1043:
765:, which states that the time reversed solution of a
1138:
Non-linear Time Series: A Dynamical System
Approach
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199:
131:
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940:"Time Reversal of Random Walks in One-Dimension"
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77:is time-reversible if the forward evolution is
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174:of all the particles of the system, i.e.
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751:piecewise deterministic Markov processes
132:{\displaystyle U_{-t}=\pi \,U_{t}\,\pi }
27:Type of physical or mathematical process
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14:
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285:for all practical considerations (see
142:Any time-independent structures (e.g.
30:A mathematical or physical process is
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25:
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1001:Electronic Journal of Probability
853:"Time Reversal on Levy Processes"
193:
190:
182:
1119:Stochastic Theory and Modelling
897:Advances in Applied Probability
851:Jacod, J.; Protter, P. (1988).
781:Time reversal signal processing
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1047:Smart Materials and Structures
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978:. Cambridge University Press.
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895:(1976). "Networks of Queues".
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256:, depending on the change in
230:of the spatial co-ordinates (
944:Tokyo Journal of Mathematics
724:continuous-time Markov chain
718:defines the condition for a
7:
787:
277:statistics of the ensembles
10:
1189:
1121:, Hinkley, DV., Reid, N.,
769:is also a solution to the
287:Crooks fluctuation theorem
153:
1125:(Eds). Chapman and Hall.
857:The Annals of Probability
743:birth and death processes
282:statistical impossibility
841:Tong (1990), Section 4.4
814:
575:A univariate stationary
726:to be time-reversible.
263:artificial intelligence
246:Thermodynamic processes
1099:, 4 (1), 5-16 (2008).
957:10.3836/tjm/1270133555
870:10.1214/aop/1176991776
716:Kolmogorov's criterion
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267:macroscopic properties
218:systems, however, the
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53:under a change in the
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39:deterministic process
1023:10.1214/EJP.v18-1958
809:Reversible computing
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579:is time-reversible.
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314:= 1, ...,
293:Stochastic processes
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1059:2016SMaS...25h5015P
938:Tanaka, H. (1989).
735:stochastic networks
168:classical mechanics
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299:stochastic process
220:weak nuclear force
216:quantum mechanical
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59:stochastic process
18:Time-reversibility
1163:Dynamical systems
1131:978-0-412-30590-0
172:conjugate momenta
43:dynamic equations
16:(Redirected from
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747:Markov chains
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240:CPT symmetry
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1157:Categories
1110:References
863:(2): 620.
794:T-symmetry
250:reversible
236:P-symmetry
232:C-symmetry
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