Entropy and Thermodynamic Temperature in Nonequilibrium Classical Thermodynamics as Immediate Consequences of the Hahn-Banach Theorem: I. Existence

2023/08/16 by Feinberg, Martin, Lavine, Richard B. · 1 citation
#Chemical Physics (physics.chem-ph) #Classical Physics (physics.class-ph) #FOS: Biological sciences #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Molecular Networks (q-bio.MN)

paper · doi:10.48550/arxiv.2308.08636

Abstract

The Kelvin-Planck statement of the Second Law of Thermodynamics is a stricture on the nature of heat receipt by any body suffering a cyclic process. It makes no mention of temperature or of entropy. Beginning with a Kelvin-Planck statement of the Second Law, we show that entropy and temperature -- in particular, existence of functions that relate the local specific entropy and thermodynamic temperature to the local state in a material body -- emerge immediately and simultaneously as consequences of the Hahn-Banach Theorem. Existence of such functions of state requires no stipulation that their domains be restricted to equilibrium states. Further properties, including uniqueness, are addressed in a companion paper.

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