The different paths to entropy

TL;DR

This paper explores the historical development of entropy by reviewing key contributions from Clausius, Boltzmann, Gibbs, and Planck, highlighting different conceptualizations and their implications for thermodynamics and irreversibility.

Contribution

It provides a detailed analysis of Gibbs's three definitions of entropy and discusses entropy as a thermodynamic potential, offering new insights into its conceptual evolution.

Findings

Gibbs's three definitions of entropy are clarified and compared.

Entropy can be viewed as a thermodynamic potential similar to other potentials.

Remarks on the relationship between entropy and irreversibility are provided.

Abstract

In order to undestand how the complex concept of entropy emerged,we propose a trip towards the past reviewing the works of Clausius, Boltzmann, Gibbs and Planck. In particular, since the Gibbs's work is not very well known, we present a detailed analysis, recalling the three definitions of the entropy that Gibbs gives. May be one of the most important aspect of the entropy is to see it as a thermodynamic potential like the other thermodynamic potentials as proposed by Callen. We close with some remarks on entropy and irreversibility.