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Atoms, Mechanics, and ProbabilityLudwig Boltzmann's Statistico-Mechanical Writings - An Exegesis$
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Olivier Darrigol

Print publication date: 2018

Print ISBN-13: 9780198816171

Published to Oxford Scholarship Online: March 2018

DOI: 10.1093/oso/9780198816171.001.0001

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The Boltzmann Equation and the H Theorem (1872–1875)

The Boltzmann Equation and the H Theorem (1872–1875)

Chapter:
(p.134) 4 The Boltzmann Equation and the H Theorem (1872–1875)
Source:
Atoms, Mechanics, and Probability
Author(s):

Olivier Darrigol

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198816171.003.0004

This chapter covers Boltzmann’s writings about the Boltzmann equation and the H theorem in the period 1872–1875, through which he succeeded in deriving the irreversible evolution of the distribution of molecular velocities in a dilute gas toward Maxwell’s distribution. Boltzmann also used his equation to improve on Maxwell’s theory of transport phenomena (viscosity, diffusion, and heat conduction). The bulky memoir of 1872 and the eponymous equation probably are Boltzmann’s most famous achievements. Despite the now often obsolete ways of demonstration, despite the lengthiness of the arguments, and despite hidden difficulties in the foundations, Boltzmann there displayed his constructive skills at their best.

Keywords:   Boltzmann equation, collisions number, H theorem, irreversibility, transport phenomena

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