publication . Article . Other literature type . 1965

gibbs vs boltzmann entropies

Jaynes, E. T.;
Open Access
  • Published: 01 May 1965 Journal: American Journal of Physics, volume 33, pages 391-398 (issn: 0002-9505, eissn: 1943-2909, Copyright policy)
  • Publisher: American Association of Physics Teachers (AAPT)
The status of the Gibbs and Boltzmann expressions for entropy has been a matter of some confusion in the literature. We show that: (1) the Gibbs H function yields the correct entropy as defined in phenomenological thermodynamics; (2) the Boltzmann H yields an “entropy” that is in error by a nonnegligible amount whenever interparticle forces affect thermodynamic properties; (3) Boltzmann's other interpretation of entropy, S = k log W, is consistent with the Gibbs H, and derivable from it; (4) the Boltzmann H theorem does not constitute a demonstration of the second law for dilute gases; (5) the dynamical invariance of the Gibbs H gives a simple proof of the secon...
free text keywords: General Physics and Astronomy, Boltzmann's entropy formula, H-theorem, Entropy (statistical thermodynamics), Maximum entropy thermodynamics, Physics, Gibbs paradox, symbols.namesake, symbols, Entropy (arrow of time), Entropy (classical thermodynamics), Entropy in thermodynamics and information theory, Statistical physics
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