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Ludwig BoltzmannThe Man Who Trusted Atoms$
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Carlo Cercignani

Print publication date: 2006

Print ISBN-13: 9780198570646

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780198570646.001.0001

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Boltzmann, Gibbs, and equilibrium statistical mechanics

Boltzmann, Gibbs, and equilibrium statistical mechanics

(p.134) 7 Boltzmann, Gibbs, and equilibrium statistical mechanics
Ludwig Boltzmann


Oxford University Press

This chapter discusses equilibrium statistical mechanics for systems more complicated than monatomic gases, as well as the problem of the trend towards equilibrium of these systems. Ludwig Boltzmann is credited for having begun this branch of statistical mechanics with a basic paper written in 1884, in which he formulated the hypothesis that some among the possible steady distributions can be interpreted as macroscopic equilibrium states. This fundamental work by Boltzmann was taken up again, widened, and expounded in a classical treatise by Josiah Willard Gibbs. In his paper, Boltzmann described statistical families of steady distributions, which he called orthodes. Boltzmann showed that there are at least two ensembles of this kind, the ergode (Gibbs's microcanonical ensemble) and the holode (Gibbs's canonical ensemble). This article also explains why statistical mechanics is usually attributed to Gibbs and not to Boltzmann, the problem of trend to equilibrium and ergodic theory, and Max Planck's work on statistical mechanics.

Keywords:   gases, Josiah Willard Gibbs, Max Planck, equilibrium statistical mechanics, equilibrium states, orthodes, ergode, holode

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