Entropy formula of N-body system

Abstract We prove a proposition that the entropy of the system composed of finite N molecules of ideal gas is the q-entropy or Havrda–Charvát–Tsallis entropy, which is also known as Tsallis entropy, with the entropic index $$q=\frac{D(N-1)-4}{D(N-1)-2}$$ q = D ( N - 1 ) - 4 D ( N - 1 ) - 2 in D-dime...

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Autor principal:	Jae Wan Shim
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2020
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/9dbed3130c6f4df7834abb8865269f82
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spelling	oai:doaj.org-article:9dbed3130c6f4df7834abb8865269f822021-12-02T16:46:34ZEntropy formula of N-body system10.1038/s41598-020-71103-w2045-2322https://doaj.org/article/9dbed3130c6f4df7834abb8865269f822020-08-01T00:00:00Zhttps://doi.org/10.1038/s41598-020-71103-whttps://doaj.org/toc/2045-2322Abstract We prove a proposition that the entropy of the system composed of finite N molecules of ideal gas is the q-entropy or Havrda–Charvát–Tsallis entropy, which is also known as Tsallis entropy, with the entropic index $$q=\frac{D(N-1)-4}{D(N-1)-2}$$ q = D ( N - 1 ) - 4 D ( N - 1 ) - 2 in D-dimensional space. The indispensable infinity assumption used by Boltzmann and others in their derivation of entropy formulae is not involved in our derivation, therefore our derived formula is exact. The analogy of the N-body system brings us to obtain the entropic index of a combined system $$q_C$$ q C formed from subsystems having different entropic indexes $$q_A$$ q A and $$q_B$$ q B as $$\frac{1}{1-q_C}=\frac{1}{1-q_A}+\frac{1}{1-q_B}+\frac{D+2}{2}$$ 1 1 - q C = 1 1 - q A + 1 1 - q B + D + 2 2 . It is possible to use the number N for the physical measure of deviation from Boltzmann entropy.Jae Wan ShimNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 10, Iss 1, Pp 1-3 (2020)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Jae Wan Shim Entropy formula of N-body system
description	Abstract We prove a proposition that the entropy of the system composed of finite N molecules of ideal gas is the q-entropy or Havrda–Charvát–Tsallis entropy, which is also known as Tsallis entropy, with the entropic index $$q=\frac{D(N-1)-4}{D(N-1)-2}$$ q = D ( N - 1 ) - 4 D ( N - 1 ) - 2 in D-dimensional space. The indispensable infinity assumption used by Boltzmann and others in their derivation of entropy formulae is not involved in our derivation, therefore our derived formula is exact. The analogy of the N-body system brings us to obtain the entropic index of a combined system $$q_C$$ q C formed from subsystems having different entropic indexes $$q_A$$ q A and $$q_B$$ q B as $$\frac{1}{1-q_C}=\frac{1}{1-q_A}+\frac{1}{1-q_B}+\frac{D+2}{2}$$ 1 1 - q C = 1 1 - q A + 1 1 - q B + D + 2 2 . It is possible to use the number N for the physical measure of deviation from Boltzmann entropy.
format	article
author	Jae Wan Shim
author_facet	Jae Wan Shim
author_sort	Jae Wan Shim
title	Entropy formula of N-body system
title_short	Entropy formula of N-body system
title_full	Entropy formula of N-body system
title_fullStr	Entropy formula of N-body system
title_full_unstemmed	Entropy formula of N-body system
title_sort	entropy formula of n-body system
publisher	Nature Portfolio
publishDate	2020
url	https://doaj.org/article/9dbed3130c6f4df7834abb8865269f82
work_keys_str_mv	AT jaewanshim entropyformulaofnbodysystem
_version_	1718383411733725184

Entropy formula of N-body system

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