DOI: 10.1119/1.1971557. Gibbs vs Boltzmann Entropies

10.1119/1.1971557

Crossref journal-article

American Association of Physics Teachers (AAPT)

American Journal of Physics (3)

Abstract

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 second law for arbitrary interparticle forces; (6) the second law is a special case of a general requirement for any macroscopic process to be experimentally reproducible. Finally, the “anthropomorphic” nature of entropy, on both the statistical and phenomenological levels, is stressed.

Bibliography

Jaynes, E. T. (1965). Gibbs vs Boltzmann Entropies. American Journal of Physics, 33(5), 391â398.

Authors 1

E. T. Jaynes (first)

References 0 Referenced 384

None

Dates

Type	When
Created	20 years ago (Aug. 22, 2005, 3:01 p.m.)
Deposited	2 years, 1 month ago (July 13, 2023, 1:49 a.m.)
Indexed	3 days, 8 hours ago (Aug. 31, 2025, 6:30 a.m.)
Issued	60 years, 4 months ago (May 1, 1965)
Published	60 years, 4 months ago (May 1, 1965)
Published Online	20 years, 1 month ago (July 8, 2005)
Published Print	60 years, 4 months ago (May 1, 1965)

Funders 0

None

BibTeX

@article{Jaynes_1965, title={Gibbs vs Boltzmann Entropies}, volume={33}, ISSN={1943-2909}, url={http://dx.doi.org/10.1119/1.1971557}, DOI={10.1119/1.1971557}, number={5}, journal={American Journal of Physics}, publisher={American Association of Physics Teachers (AAPT)}, author={Jaynes, E. T.}, year={1965}, month=may, pages={391–398} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        8,
        31
      ]
    ],
    "date-time": "2025-08-31T10:30:00Z",
    "timestamp": 1756636200149
  },
  "reference-count": 0,
  "publisher": "American Association of Physics Teachers (AAPT)",
  "issue": "5",
  "content-domain": {
    "domain": [
      "pubs.aip.org"
    ],
    "crossmark-restriction": true
  },
  "published-print": {
    "date-parts": [
      [
        1965,
        5,
        1
      ]
    ]
  },
  "abstract": "<jats:p>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 \u201centropy\u201d that is in error by a nonnegligible amount whenever interparticle forces affect thermodynamic properties; (3) Boltzmann's other interpretation of entropy, S\u2009=\u2009k\u2009log\u2009W, 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 second law for arbitrary interparticle forces; (6) the second law is a special case of a general requirement for any macroscopic process to be experimentally reproducible. Finally, the \u201canthropomorphic\u201d nature of entropy, on both the statistical and phenomenological levels, is stressed.</jats:p>",
  "DOI": "10.1119/1.1971557",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2005,
        8,
        22
      ]
    ],
    "date-time": "2005-08-22T19:01:27Z",
    "timestamp": 1124737287000
  },
  "page": "391-398",
  "update-policy": "http://dx.doi.org/10.1063/aip-crossmark-policy-page",
  "source": "Crossref",
  "is-referenced-by-count": 384,
  "title": "Gibbs vs Boltzmann Entropies",
  "prefix": "10.1119",
  "volume": "33",
  "author": [
    {
      "given": "E. T.",
      "family": "Jaynes",
      "sequence": "first",
      "affiliation": [
        {
          "name": "Department of Physics, Washington University, St. Louis, Missouri"
        }
      ]
    }
  ],
  "member": "3",
  "published-online": {
    "date-parts": [
      [
        2005,
        7,
        8
      ]
    ]
  },
  "container-title": "American Journal of Physics",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://pubs.aip.org/aapt/ajp/article-pdf/33/5/391/12040108/391_1_online.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "syndication"
    },
    {
      "URL": "https://pubs.aip.org/aapt/ajp/article-pdf/33/5/391/12040108/391_1_online.pdf",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2023,
        7,
        13
      ]
    ],
    "date-time": "2023-07-13T05:49:24Z",
    "timestamp": 1689227364000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://pubs.aip.org/ajp/article/33/5/391/531425/Gibbs-vs-Boltzmann-Entropies"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1965,
        5,
        1
      ]
    ]
  },
  "references-count": 0,
  "journal-issue": {
    "issue": "5",
    "published-online": {
      "date-parts": [
        [
          2005,
          7,
          8
        ]
      ]
    },
    "published-print": {
      "date-parts": [
        [
          1965,
          5,
          1
        ]
      ]
    }
  },
  "URL": "http://dx.doi.org/10.1119/1.1971557",
  "relation": {},
  "ISSN": [
    "0002-9505",
    "1943-2909"
  ],
  "subject": [],
  "published-other": {
    "date-parts": [
      [
        1965,
        5
      ]
    ]
  },
  "published": {
    "date-parts": [
      [
        1965,
        5,
        1
      ]
    ]
  }
}