# Randomness and Thermodynamics

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?

• 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. – user126422 Apr 29 '17 at 16:53
• 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. – dmckee Apr 29 '17 at 17:30
• @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? – Jannik Pitt Apr 29 '17 at 18:23
• 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. – user126422 Apr 30 '17 at 0:07
• "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. – Deep Apr 30 '17 at 4:38

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.