Jump to ContentJump to Main Navigation
Ludwig BoltzmannThe Man Who Trusted Atoms$
Users without a subscription are not able to see the full content.

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

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2019. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a monograph in OSO for personal use (for details see www.oxfordscholarship.com/page/privacy-policy).date: 22 February 2019

Time irreversibility and the H-theorem

Time irreversibility and the H-theorem

(p.96) 5 Time irreversibility and the H-theorem
Ludwig Boltzmann


Oxford University Press

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

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .