Clausius' theorem and the second law in the process of isoenergetic thermalization.

Isoenergetic thermalization amongst n bodies is a well-known irreversible process, bringing the bodies to a common temperature T_{F} and leading to a rise in the total entropy of the bodies. We express this change in entropy using the Clausius formula over a reversible path connecting T_{F} with T_{f}, which corresponds to the entropy-preserving temperature of the initial nonequilibrium state. Under the assumption of positive heat capacities of the bodies, the second law inequality simply follows from the fact that T_{F}>T_{f}.