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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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Time irreversibility and the H-theorem

Time irreversibility and the H-theorem

Chapter:
(p.96) 5 Time irreversibility and the H-theorem
Source:
Ludwig Boltzmann
Author(s):

CARLO CERCIGNANI

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198570646.003.0005

Ludwig Boltzmann not only showed that his Boltzmann equation, which captures the essence of the second law of thermodynamics in mathematical form, admits James Clerk Maxwell's distribution as an equilibrium solution, but he also gave a heuristic proof that it is the only possible one. To this end he introduced a quantity, which he denoted by E and was later denoted by H, defined in terms of the molecular velocity distribution. His result is usually quoted as the H-theorem and indicates that H must be proportional to minus the entropy. The equation is the first to govern the evolution in time of a probability. The proof for the Boltzmann equation can be extended to polyatomic gases. This chapter also discusses Loschmidt's paradox, Zermelo's paradox, the physical and mathematical resolution of the paradoxes, time's arrow and the expanding universe, and whether time irreversibility is objective or subjective.

Keywords:   second law of thermodynamics, Boltzmann equation, time irreversibility, H-theorem, probability, James Clerk Maxwell, Loschmidt's paradox, Zermelo's paradox, entropy

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