Communication: system-size scaling of Boltzmann and alternate Gibbs entropies

It has recurrently been proposed that the Boltzmann textbook definition of entropy S(E) = k ln Ω(E) in terms of the number of microstates Ω(E) with energy E should be replaced by the expression S(G)(E) = k ln Σ(E' < E)Ω(E') examined by Gibbs. Here, we show that SG either is equivalent t...

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Veröffentlicht in:	The Journal of chemical physics 2014-05, Vol.140 (20), p.201101-201101
Hauptverfasser:	Vilar, Jose M G, Rubi, J Miguel
Format:	Artikel
Sprache:	eng
Schlagworte:	Cold Temperature Communications systems Computer Simulation Entropy Hot Temperature Scaling Thermodynamics
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container_title	The Journal of chemical physics
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creator	Vilar, Jose M G Rubi, J Miguel
description	It has recurrently been proposed that the Boltzmann textbook definition of entropy S(E) = k ln Ω(E) in terms of the number of microstates Ω(E) with energy E should be replaced by the expression S(G)(E) = k ln Σ(E' < E)Ω(E') examined by Gibbs. Here, we show that SG either is equivalent to S in the macroscopic limit or becomes independent of the energy exponentially fast as the system size increases. The resulting exponential scaling makes the realistic use of SG unfeasible and leads in general to temperatures that are inconsistent with the notions of hot and cold.
doi_str_mv	10.1063/1.4879553
format	Article
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Here, we show that SG either is equivalent to S in the macroscopic limit or becomes independent of the energy exponentially fast as the system size increases. The resulting exponential scaling makes the realistic use of SG unfeasible and leads in general to temperatures that are inconsistent with the notions of hot and cold.</description><identifier>ISSN: 0021-9606</identifier><identifier>EISSN: 1089-7690</identifier><identifier>DOI: 10.1063/1.4879553</identifier><identifier>PMID: 24880258</identifier><language>eng</language><publisher>United States: American Institute of Physics</publisher><subject>Cold Temperature ; Communications systems ; Computer Simulation ; Entropy ; Hot Temperature ; Scaling ; Thermodynamics</subject><ispartof>The Journal of chemical physics, 2014-05, Vol.140 (20), p.201101-201101</ispartof><rights>2014 AIP Publishing LLC.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c348t-6716de63382f3fc7f4365b4883315ac025c13695b73294ce087a3c43a18b60403</citedby><cites>FETCH-LOGICAL-c348t-6716de63382f3fc7f4365b4883315ac025c13695b73294ce087a3c43a18b60403</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27901,27902</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/24880258$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Vilar, Jose M G</creatorcontrib><creatorcontrib>Rubi, J Miguel</creatorcontrib><title>Communication: system-size scaling of Boltzmann and alternate Gibbs entropies</title><title>The Journal of chemical physics</title><addtitle>J Chem Phys</addtitle><description>It has recurrently been proposed that the Boltzmann textbook definition of entropy S(E) = k ln Ω(E) in terms of the number of microstates Ω(E) with energy E should be replaced by the expression S(G)(E) = k ln Σ(E' < E)Ω(E') examined by Gibbs. 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subjects	Cold Temperature Communications systems Computer Simulation Entropy Hot Temperature Scaling Thermodynamics
title	Communication: system-size scaling of Boltzmann and alternate Gibbs entropies
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