# Derivation of 2nd law of Thermodynamics from ergodicity assumption

In Wikipedia it is claimed that:

Assumption of the ergodic hypothesis allows proof that certain types of perpetual motion machines of the second kind are impossible.

Since perpetual motion machines are machines which would violate the 2nd law, shouldn't it then from this be possible to derive the 2nd law from the ergodic hypothesis?

• Yes, the assumption of ergodicity is part of the statistical derivation of the 2nd law, but I think you also need some assumptions about initial conditions, if I remember correctly. – Cuspy Code Nov 27 '18 at 21:18
• Could you please refer me to a book or so with the proof. I have been looking for a proof but couldn't find any. – eeqesri Nov 28 '18 at 9:09

Ergodicity is also compatible with violations of the second law of thermodynamics, because of the simple reason that if $$T_t$$ is an ergodic time-evolution which is invertible, then also $$T_{-t}$$ is ergodic. But obviously, if one of them leads to an increase in entropy, the other one violates the second law. Therefore, as said correctly in a comment above, an assumption about (typical) initial values is also necessary.