After a quench in a system, it gets turbulent and maybe goes too far from equilibrium situation, so after that, how the entropy and quench relating to each other? _ also what will happen to the information of the system?
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$\begingroup$ Can you express this in other words? I'm having trouble understanding the situation you are describing. $\endgroup$– Chet MillerCommented Dec 23, 2017 at 23:10
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$\begingroup$ As you know after a sudden change in the system ( quench ) the system tries to come back to its normal situation ( thermal equilibrium ) . So I wonder how the entropy of the system will be change to balance the system. $\endgroup$– mohammadrezaCommented Dec 24, 2017 at 9:36
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$\begingroup$ Also during this change what will happen for the information of the system.? $\endgroup$– mohammadrezaCommented Dec 24, 2017 at 9:38
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$\begingroup$ Probably the reason you haven't received any responses to your question is that we are having trouble understanding what you are describing. We are not mind readers. Can you please describe the physical situation in greater detail? $\endgroup$– Chet MillerCommented Dec 24, 2017 at 12:56
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$\begingroup$ John Von Neumann said: "..nobody knows what entropy really is, so in a debate you will always have the advantage"! $\endgroup$– SteveCommented Jan 8, 2018 at 16:21
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1 Answer
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If you are talking about a quantum quench of a pure state, the answer is as follows:
- The information of the entire system is exact, i.e. the entropy of the entire system is $0$, because the entire system is always a pure state.
- But if one takes a look at local observables, e.g. entanglement entropy of a subsystem, the entropy is non-zero, i.e. the local information is not complete (the subsystem is entangled with the rest of the system).
- Thus it is only sensible to talk about thermalisation locally. The entropy that appears in the non-equilibrium steady state ($t\rightarrow \infty$ limit) is precisely the entanglement entropy of a subsystem (usually $\mathcal{O}(\frac{1}{L})$ compared to the total system), as shown in Calabrese and Cardy. For non-integrable systems, thermalisation happens, while for integrable systems, generalised thermalisation (steady state is described by generalised Gibbs ensemble) happens.
