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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’s relation and the statistical interpretation of entropy

Boltzmann’s relation and the statistical interpretation of entropy

Chapter:
(p.120) 6 Boltzmann’s relation and the statistical interpretation of entropy
Source:
Ludwig Boltzmann
Author(s):

CARLO CERCIGNANI

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198570646.003.0006

Ludwig Boltzmann first used probabilistic arguments in his answer to Johann Loschmidt's objection to his Boltzmann equation and his assumptions about entropy in the H-theorem. Up to that moment, although he mentioned probability in his papers, Boltzmann seemed to think that the distribution function was a way of utilising the techniques of mathematical analysis in order to count the actual numbers of molecules, and no hidden probabilistic assumption was contained in his arguments. If Boltzmann had already begun to hint at the important role of probability in 1871, the priority in stressing the necessity of a statistical interpretation of the second law of thermodynamics must certainly be credited to James Clerk Maxwell because of his invention of the demon now named after him. This chapter discusses the probabilistic interpretation of thermodynamics, explicit use of probability for a gas with discrete energies, energy as a continuous phemonenon, and the so-called H-curve.

Keywords:   H-theorem, probability, entropy, H-curve, Boltzmann equation, distribution function, James Clerk Maxwell, molecules, thermodynamics, energy

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