Rigorous information-theoretic derivation of quantum-statistical thermodynamics. II

Abstract

Part I of the present work outlined the rigorous application of information theory to a quantum mechanical system in a thermodynamic equilibrium state. The general formula developed there for the best-guess density operator$\hat \rho$ was indeterminate because it involved in an essential way an unspecified prior probability distribution over the continuumD _H of strong equilibrium density operators. In Part II mathematical evaluation of$\hat \rho$ is completed after an epistemological analysis which leads first to the discretization ofD _H and then to the adoption of a suitable indifference axiom to delimit the set of admissible prior distributions. Finally, quantal formulas for information-theoretic and thermodynamic entropies are contrasted, and the entire work is summarized.