Recent Progress in the Definition of Thermodynamic Entropy

Abstract

The principal methods for the definition of thermodynamic entropy are discussed with special reference to those developed by Carathéodory, the Keenan School, Lieb and Yngvason, and the present authors. An improvement of the latter method is then presented. Seven basic axioms are employed: three Postulates, which are considered as having a quite general validity, and four Assumptions, which identify the domains of validity of the definitions of energy (Assumption 1) and entropy (Assumptions 2, 3, 4). The domain of validity of the present definition of entropy is not restricted to stable equilibrium states. For collections of simple systems, it coincides with that of the proof of existence and uniqueness of an entropy function which characterizes the relation of adiabatic accessibility proposed by Lieb and Yngvason. However, our treatment does not require the formation of scaled copies so that it applies not only to collections of simple systems, but also to systems contained in electric or magnetic fields and to small and few-particle systems.

arXiv comment23 pages, 5 figures

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• Steepest-entropy-ascent quantum thermodynamic modeling of heat and mass diffusion in a far-from-equilibrium system based on a single particle ensemble
• Thermodynamics from relative entropy
• Steepest-entropy-ascent quantum thermodynamic modeling of the far-from-equilibrium interactions between nonequilibrium systems of indistinguishable particle ensembles
• Entropy Meters and the Entropy of Non-extensive Systems
• A Method for Predicting Nonequilibrium Thermal Expansion Using Steepest-Entropy-Ascent Quantum Thermodynamics
• Uniqueness of solutions in thermopiezoelectricity of nonsimple materials
• Smooth entropy in axiomatic thermodynamics