Classical thermodynamics always discusses entropy in the light of reversible processes, and it lies at the heart of the definition of entropy. But do these reversible processes exist in Nature, or are they just a gedankenexperiment?

Since if they do not exist, then classical thermodynamics gives a lower bound on the increase of entropy, but says nothing about the difference in entropy between the reversible and irreversible process. Doesn't this make the classical definition useless for a quantitative approach? Or is there proof that the entropy difference between the reversible and irreversible process is small for most everyday cases?

  • $\begingroup$ Most of the processes we are aware of have $T$ symmetry! $\endgroup$ – Ali May 3 '14 at 16:37
  • $\begingroup$ Some quantum systems can reversible flip between two states, for example Benzene rings. But this is far from the statistical definition of entropy that you are interested. I'm not aware of any physical system or thermodynamic engine which can be made completely reversible (i.e. operate at the Carnot limit), it's probably impossible. Carnot efficiency give the maximum efficiency of a heat energy and therefore the minimum amount if entropy that needs to be generated. $\endgroup$ – boyfarrell May 5 '14 at 5:02

Of course, thermodynamics says things about differences in entropy between reversible and irreversible processes. In fact, we can analyse how irreversible a process was and what to do in order to, for instance, extract more work from it. That's a very important part of thermodynamics.

But, no, there are no truly reversible processes — at least for daily macroscopic, bulk phenomena; I might be unaware of some crazy quantum-relativistic-boson-fermion experiment :). In practice, all real processes are irreversible, even though some can be good approximations of reversible ones (e.g. if you go really slowly).

Also, your statement "classical thermodynamics gives a lower bound on the increase of entropy" is a bit weird. That "lower bound" would be zero, so I'd prefer to say that it states that global entropy never decreases. Apart from that, classical thermodynamics also goes on to explore quantities like availability, irreversibility and efficiency, and it can do a good work of optimizing the hell out of your irreversible processes.

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    $\begingroup$ "all real processes are irreversible" should probably be revised to "all real thermodynamic processes are irreversible". After all, that's the primary conceptual difficulty with thermodynamics; it imposes a macroscopic time-reversal asymmetry, while microscopically, everything is time-reversal symmetric. (The Standard Model has $CPT$ symmetry, after all.) $\endgroup$ – probably_someone Jun 8 '18 at 16:15

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