Formulation of Entropy through Work by Carnot Machine and Direct Derivation of Law of Entropy Non-Decrease from Kelvin-Planck Principle

2024/11/11 by Yuki Izumida, Izumida, Yuki
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)

paper · pdf · doi:10.48550/arxiv.2411.07438

openalex publication_date 2024/11/11 · openalex created_date 2024/11/16 · openalex updated_date 2026/07/28

Abstract

We derive the law of entropy non-decrease directly from the Kelvin-Planck principle for simple and compound systems without using the Clausius inequality. A key of the derivation is a new formulation of entropy in terms of work by a Carnot machine operating between a system and a single heat reservoir at fixed temperature, which is equivalent to Clausius entropy based on heat and Gyftopoulos-Beretta entropy based on work. We also show that we may characterize entropy as an extra thermodynamic cost that needs to be paid to create nonuniformity in the system.

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