Quantum Purity as an Information Measure and Nernst law

Abstract

We attempt to re-express Nernst law in terms of a suitable information measure (IM). This is done on the basis of adapting the idea of purity to a thermal Gibbs environment, which yields what we might call a ``purity'' (and symbolize it by the symbol $D$). We further apply the properly generalization of this $D$-IM to a classical scenario.
 This generalization turns our to have interesting consequences, when used in conjunction with the classical Shannon entropy $S$. These consequences are related to Nernst law.