Boltzmann's Entropy and Time's Arrow

TLDR

Boltzmann’s statistical mechanics successfully explains macroscopic irreversibility, yet confusion and controversies—stemming from the originality of his ideas and misunderstandings by contemporaries—persist despite his clear later writings. The paper reviews Boltzmann’s concepts of the arrow of time in celebration of his 150th birth anniversary. The author finds that alleged inconsistencies with Boltzmann’s theory are unfounded and no alternative explanations are required. See figure 1; further reading includes Boltzmann’s works and references 2–7, plus a 1992 Physics Today article.

Abstract

Given the success of Ludwig Boltzmann's statistical approach in explaining the observed irreversible behavior of macroscopic systems in a manner consistent with their reversible microscopic dynamics, it is quite surprising that there is still so much confusion about the problem of irreversibility. (See figure 1.) I attribute this confusion to the originality of Boltzmann's ideas: It made them difficult for some of his contemporaries to grasp. The controversies generated by the misunderstandings of Ernst Zermelo and others have been perpetuated by various authors. There is really no excuse for this, considering the clarity of Boltzmann's later writings. Since next year, 1994, is the 150th anniversary of Boltzmann's birth, this is a fitting moment to review his ideas on the arrow of time. In Erwin Schrödinger's words, “Boltzmann's ideas really give an understanding” of the origin of macroscopic behavior. All claims of inconsistencies that I know of are, in my opinion, wrong; I see no need for alternate explanations. for further reading I highly recommend Boltzmann's works as well as references 2–7. (See also PHYSICS TODAY, January 1992, page 44, for a marvelous description by Boltzmann of his visit to California in 1906.)