Formulation of entropy through work by Carnot machine and direct derivation of law of entropy non-decrease from Kelvin-Planck principle (2411.07438v6)

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 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 the extra thermodynamic cost that needs to be paid to create nonuniformity in the system.