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

TL;DR

This paper introduces a new formulation of entropy based on work done by a Carnot machine and derives the law of entropy non-decrease directly from the Kelvin-Planck principle, avoiding the Clausius inequality.

Contribution

It presents a novel formulation of entropy in terms of work and directly derives the entropy non-decrease law from fundamental principles.

Findings

Entropy can be formulated via work by a Carnot machine.

The law of entropy non-decrease is derived directly from Kelvin-Planck principle.

Entropy characterized as a thermodynamic cost for creating nonuniformity.

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.