The Use of the Information Theoretic Entropy in Thermodynamics

When considering controversial thermodynamic scenarios such as Maxwell’s demon, it is often necessary to consider probabilistic mixtures of states. This raises the question of how, if at all, to assign entropy to them. The information-theoretic entropy is often used in such cases; however, no general proof of the soundness of doing so has been given, and indeed some arguments against doing so have been presented. We offer a general proof of the applicability of the information-theoretic entropy to probabilistic mixtures of macrostates, making clear the assumptions on which it depends, in particular a probabilistic version of the Kelvin statement of the Second Law. We briefly discuss the interpretation of our result.