{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T03:27:55Z","timestamp":1788233275877,"version":"build-2803163510"},"reference-count":18,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2017,1,24]],"date-time":"2017-01-24T00:00:00Z","timestamp":1485216000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We start with a clear distinction between Shannon\u2019s Measure of Information (SMI) and the Thermodynamic Entropy. The first is defined on any probability distribution; and therefore it is a very general concept. On the other hand Entropy is defined on a very special set of distributions. Next we show that the Shannon Measure of Information (SMI) provides a solid and quantitative basis for the interpretation of the thermodynamic entropy. The entropy measures the uncertainty in the distribution of the locations and momenta of all the particles; as well as two corrections due to the uncertainty principle and the indistinguishability of the particles. Finally we show that the H-function as defined by Boltzmann is an SMI but not entropy. Therefore; much of what has been written on the H-theorem is irrelevant to entropy and the Second Law of Thermodynamics.<\/jats:p>","DOI":"10.3390\/e19020048","type":"journal-article","created":{"date-parts":[[2017,1,24]],"date-time":"2017-01-24T10:20:29Z","timestamp":1485253229000},"page":"48","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":53,"title":["Entropy, Shannon\u2019s Measure of Information and Boltzmann\u2019s H-Theorem"],"prefix":"10.3390","volume":"19","author":[{"given":"Arieh","family":"Ben-Naim","sequence":"first","affiliation":[{"name":"Department of Physical Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2017,1,24]]},"reference":[{"key":"ref_1","unstructured":"Shannon, C.E., and Weaver, W. (1949). The Mathematical Theory of Communication, The University of Illinois Press."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Ben-Naim, A. (2017). Information Theory, World Scientific.","DOI":"10.1142\/10417"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Ben-Naim, A. (2008). A Farewell to Entropy: Statistical Thermodynamics Based on Information, World Scientific.","DOI":"10.1142\/9789812790736"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Ben-Naim, A., and Casadei, D. (2016). Modern Thermodynamics, World Scientific.","DOI":"10.1142\/10300"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Ben-Naim, A. (2012). Entropy and the Second Law. Interpretation and Misss-Interpretationsss, World Scientific.","DOI":"10.1142\/8333"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Ben-Naim, A. (2015). Discover Probability. How to Use It, How to Avoid Misusing It, and How It Affects Every Aspect of Your Life, World Scientific.","DOI":"10.1142\/9227"},{"key":"ref_7","unstructured":"Jain, V.K., and Reidel, D. (1983). Probability and Information, Springer Science & Business Media."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Ben-Naim, A. (2015). Information, Entropy, Life and the Universe. What We Know and What We Do Not Know, World Scientific.","DOI":"10.1142\/9479"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"620","DOI":"10.1103\/PhysRev.106.620","article-title":"Information theory and statistical mechanics","volume":"106","author":"Jaynes","year":"1957","journal-title":"Phys. Rev."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1103\/PhysRev.108.171","article-title":"Information theory and statistical mechanics, Part II","volume":"108","author":"Jaynes","year":"1957","journal-title":"Phys. Rev."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1126","DOI":"10.1119\/1.2338545","article-title":"The entropy of mixing and assimilation: An information-theoretical perspective","volume":"74","year":"2006","journal-title":"Am. J. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1021\/ed086p99","article-title":"An Informational-Theoretical Formulation of the Second Law of Thermodynamics","volume":"86","year":"2009","journal-title":"J. Chem. Educ."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Ben-Naim, A. (2016). Entropy, the Truth the Whole Truth and nothing but the Truth, World Scientific.","DOI":"10.1142\/10226"},{"key":"ref_14","unstructured":"Boltzmann, L. (2012). Lectures on Gas Theory, Dover Publications."},{"key":"ref_15","unstructured":"Brush, S.G. (1976). The Kind of Motion We Call Heat. A History of the Kinetic Theory of Gases in the 19th Century, Book 2: Statistical Physics and Irreversible Processes, North-Holland Publishing Company."},{"key":"ref_16","unstructured":"Brush, S.G. (1983). Statistical Physics and the Atomic Theory of Matter, from Boyle and Newton to Landau and Onsager, Princeton University Press."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Ben-Naim, A. (2010). Discover Entropy and the Second Law of Thermodynamics. A Playful Way of Discovering a Law of Nature, World Scientific.","DOI":"10.1142\/7694"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"594","DOI":"10.1021\/ed100922x","article-title":"Entropy: Order or Information","volume":"88","year":"2011","journal-title":"J. Chem. Educ."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/2\/48\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:26:53Z","timestamp":1760207213000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/2\/48"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,1,24]]},"references-count":18,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2017,2]]}},"alternative-id":["e19020048"],"URL":"https:\/\/doi.org\/10.3390\/e19020048","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,1,24]]}}}