# Can a system reach equilibrium using only reversible processes?

Consider an isolated system. We know that it will reach equilibrium after enough time. According to what I have read so far, the system should undergo irreversible processes to reach equilibrium, but is there any counterexample to this statement? i.e a system and a nonequilibrium initial condition such that processes used to reach equilibrium are all reversible?

• Not if the system is isolated. – Chet Miller Mar 13 at 14:03
• @ChetMiller Why? and what is an example if it is not isolated? – onurcanbektas Mar 13 at 14:20
• Well, if it is not isolated, then you can make the process reversible by exchanging heat and work reversibly with the surroundings. – Chet Miller Mar 13 at 15:03

Assume an isolated system. Start from an equilibrium state $$0$$ and remove some internal constraint so that the system spontaneously moves to another equilibrium state $$1$$. The difference in entropy $$\Delta S = S_1 - S_0$$ between the entropies of the final $$S_1$$ and initial $$S_0$$ is never negative (2nd law), and it is positive for an irreversible process the amount being characteristic and a measure of irreversibility.
• @Bob_D That is OK, just measure the entropy variation at any instant after the system is allowed to equilibrate and has left state $0$. – hyportnex Mar 13 at 17:34