Contemporary Reaction to Gibbs's Statistical Mechanics

TL;DR

This paper examines the early 20th-century scholarly response to Gibbs's 1902 work on statistical mechanics, highlighting its reception, critiques, and subsequent developments by notable physicists and mathematicians.

Contribution

It analyzes the initial reactions and adaptations of Gibbs's statistical mechanics, revealing how it influenced and diverged from Boltzmann's theories in the early scientific community.

Findings

Gibbs's approach was praised for its rigor and foundation.

Some critics found Gibbs's work difficult to understand.

Development of applications like grand canonical ensembles and critical phenomena.

Abstract

J. Willard Gibbs published a book in 1902 on statistical mechanics that quickly received significant attention from his contemporaries because of the reputation that he had secured with his prior work on thermodynamics. People reading Gibbs's book were often familiar with Ludwig Boltzmann's work on the kinetic theory of gases. This article looks at the published response to Gibbs's book in the decade following its publication. What did these readers get from reading Elementary Principles in Statistical Mechanics? How did they put that to use? Was it fruitful? Samuel H. Burbury had been strongly critical of the assumptions on which Boltzmann's theory was built and had expressed a need for a theory without them. Burbury was pleased with the foundation and rigor of Gibbs's approach, since in his first three chapters he had built on analytical mechanics in the Hamiltonian formulation, a many-body dynamical system. Others found Gibbs hard to understand and some were critical. Hendrik A. Lorentz began teaching Gibbs's dynamical theory and supervised a thesis by Leonard Ornstein in which Orenstein developed applications built on grand canonical ensembles and correlations, which were contrary to Boltzmann's molecular disorder. Ornstein and Zernike expanded on material in that thesis to develop a theory of critical opalescence without infinities.