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Fluctuation theorems are (also) concerned with defining work in the non-equilibrium regime.

Now I've read that in regimes where Fluctuations become very strong (which I assume are the non-equilibrium regime and regimes of very small scales such as quantum regime) thermodyanmic quantities such as work or heat become random variables.

On these very short (quantum) length scales, thermal as well as quantum fluctuations become important, and usual thermodynamic quantities, such as work and heat, acquire a stochastic nature.

I'd like to discuss the implications of this. What does it mean if work is a stochastic quantity?

To better understand this I was thinking of a mini-cilinder, where we change some external parameter such as the volume by pushing in a piston. Apparently the stochasatic nature would imply that if we push in the piston with the same force multiple times the work performed by/on the system can be different from case to case. And only in limits of large repetitions we get a average value which is somewhat reliable.

Is this the correct way to think about it? (mind you for now I am only interested in work).

Also: Does this stochastic nature only occur on small quantum scales, or is this the case for non-equilibrium regime aswell?

Thanks in advance!

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    $\begingroup$ Search about Jarzynski equality and Crooks relation. They deal exactly with this, with implication to second law of thermodynamics. $\endgroup$ – Alexander Jan 28 '19 at 18:41
  • $\begingroup$ Quick hint : Assuming system under consideration is isolated. (i) Every time system is prepared, its microstate varies (same source of randomness as for classical setup) . (ii) For quantum case, work (so as to satisfy FT of Jarzynski/Bochkov-Kuzelov) is defined through two energy measurements, this is another source of randomness (unique for quantum case). $\endgroup$ – Sunyam Jan 29 '19 at 5:55

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