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I am currently reading The road to reality by Roger Penrose. In chapter 27 he discusses time symmetry in dynamic evolution. He defines the Second Law of thermodynamics the following way:

Heat flows from a hotter to a colder body.

He states that this law implies time asymmetry: When you look at a system of two bodies, one colder than the other, the hotter body will become colder and the heat will transfer to the other body until they are in equilibrium. The system evolves perfectly deterministically. But when you look at the system backwards, the two bodies are in equilibrium and after some time suddenly one body will get colder and the other one will get hotter.

Now my question: In a universe where time evolution is reversed would such a process be perceived as a random process with no deterministic cause? In a two body system in equilibrium one body would suddenly get colder and the other one hotter. But in this universe it can not be determined which body will get colder and when - it is essentially a random process. If the theoretical inhabitants of this universe looked at this process backwards, they could not really recover the Second Law of Thermodynamics. From their viewpoint they could only state that the body that ends up hotter after the equilibrium breaks will get hotter.

Is it possible that there are such "hidden laws" that underlie a process, but cannot be determined because their dynamical evolution is hidden similarly to the process described above?

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    $\begingroup$ The second law is a statistical law, it tells you what is most likely to happen. The "spontaneous" break of equilibrium will still be deterministic. If you could measure all variables with enough precision (impossible in practice though), you would be able to predict which body will become hotter, when, and by how much. $\endgroup$
    – user126422
    Commented Apr 29, 2017 at 16:53
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    $\begingroup$ It is worth noting that the statistical mechanics predicts the size of thermal fluctuations (in various variables, but we're talking about energy here) and that these fluctuation have been measured in the laboratory and agree with the predictions. My college thermo professor called the earliest such measurements 'a tour de force in experimental technique' in a booming Germanic bass. I think he said the earliest such measurements were done in the 1970s. $\endgroup$
    – dmckee --- ex-moderator kitten
    Commented Apr 29, 2017 at 17:30
  • $\begingroup$ @WillyBillyWilliams Well as I understand it, you cannot determine which of the two bodies will get colder. Both bodies are in perfect equilibrium, how would you determine when and which body gets cooler/hotter? $\endgroup$
    – Jannik Pitt
    Commented Apr 29, 2017 at 18:23
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    $\begingroup$ If you knew the position and velocity of every particle and fields, or whatever microscopic objects you have, and the laws, why would you not? But you are correct that if your measurements are only macroscopic, then of course, because thermodynamics is an irreversible theory. $\endgroup$
    – user126422
    Commented Apr 30, 2017 at 0:07
  • $\begingroup$ "From their viewpoint they could only state that the body that ends up hotter after the equilibrium breaks will get hotter" This gives those inhabitants a time asymmetric process. Of course before a break in equilibrium occurred, there was no way to tell the direction of time just by looking at those two bodies. But there must other time asymmetric processes in their universe (running backward of course) that will help them out. $\endgroup$
    – Deep
    Commented Apr 30, 2017 at 4:38

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Probably a more interesting question is: How can these hypothetical inhabitants observe or think?

If thoughts are also time reversed, whatever that means, the mental states of the observers go from (0) seeing that the system reached equilibrium to (1) watching the equilibration process to (2) expecting that heat transfer will take place. So they're not surprised, unless they have a memory of their future.

That's, of course, supposing that mental states are well defined and that the sense of present would be preserved, which is not obviously the case $-$ after all, synapses and electrical impulses are also backwards.

These inhabitants' eyes shoot light rays instead of absorbing them: Nerve impulses come through the optical nerves and a series of inverse chemical reactions culminate with the retinal changing its structure, causing the pigment opsin to emit a light pulse.

Another important question is: how exactly is the time evolution reversed? The nature of the mechanism responsible for this change is likely to strongly influence the answers to these questions. Actually, without this mechanism being specified, I'm not really sure that's a physics question at all.

Now, if the observers are "normal" and the time is reversed only in an experiment of theirs, then, as others pointed out in the comments, the second law is a statistical law: it does't prohibit weird stuff from happening, only posits it's incredibly unlikely it will. From a microscopic point of view, the system has been put in an extremely special state, one that leads to heat being conducted along the heat gradient, instead of against it.

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