Beyond Gibbs-Boltzmann-Shannon: General Entropies -- The Gibbs-Lorentzian Example
We propose a generalisation of Gibbs' statistical mechanics into the domain of non-negligible phase space correlations. Derived are the probability distribution and entropy as a generalised ensemble average, replacing Gibbs-Boltzmann-Shannon's entropy definition enabling construction of...
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doaj-8aa11a04424a453392cd26e2af4ed5be2020-11-24T22:25:48ZengFrontiers Media S.A.Frontiers in Physics2296-424X2014-08-01210.3389/fphy.2014.00049109284Beyond Gibbs-Boltzmann-Shannon: General Entropies -- The Gibbs-Lorentzian ExampleRudolf A. Treumann0Wolfgang eBaumjohann1Dept. Geophysics Environmental Sciences, Munich University, MunichAustrian Academy of SciencesWe propose a generalisation of Gibbs' statistical mechanics into the domain of non-negligible phase space correlations. Derived are the probability distribution and entropy as a generalised ensemble average, replacing Gibbs-Boltzmann-Shannon's entropy definition enabling construction of new forms of statistical mechanics. The general entropy may also be of importance in information theory and data analysis. Application to generalised Lorentzian phase space elements yields the Gibbs-Lorentzian power law probability distribution and statistical mechanics. The corresponding Boltzmann, Fermi and Bose-Einstein distributions are found. They apply only to finite temperature states including correlations. As a by-product any negative absolute temperatures are categorically excluded, supporting a recent ``no-negative $T$ claim.http://journal.frontiersin.org/Journal/10.3389/fphy.2014.00049/fullInformation TheoryentropyStatistical Mechanicsmaximum entropyGeneralised Lorentzian distributions |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Rudolf A. Treumann Wolfgang eBaumjohann |
spellingShingle |
Rudolf A. Treumann Wolfgang eBaumjohann Beyond Gibbs-Boltzmann-Shannon: General Entropies -- The Gibbs-Lorentzian Example Frontiers in Physics Information Theory entropy Statistical Mechanics maximum entropy Generalised Lorentzian distributions |
author_facet |
Rudolf A. Treumann Wolfgang eBaumjohann |
author_sort |
Rudolf A. Treumann |
title |
Beyond Gibbs-Boltzmann-Shannon: General Entropies -- The Gibbs-Lorentzian Example |
title_short |
Beyond Gibbs-Boltzmann-Shannon: General Entropies -- The Gibbs-Lorentzian Example |
title_full |
Beyond Gibbs-Boltzmann-Shannon: General Entropies -- The Gibbs-Lorentzian Example |
title_fullStr |
Beyond Gibbs-Boltzmann-Shannon: General Entropies -- The Gibbs-Lorentzian Example |
title_full_unstemmed |
Beyond Gibbs-Boltzmann-Shannon: General Entropies -- The Gibbs-Lorentzian Example |
title_sort |
beyond gibbs-boltzmann-shannon: general entropies -- the gibbs-lorentzian example |
publisher |
Frontiers Media S.A. |
series |
Frontiers in Physics |
issn |
2296-424X |
publishDate |
2014-08-01 |
description |
We propose a generalisation of Gibbs' statistical mechanics into the domain of non-negligible phase space correlations. Derived are the probability distribution and entropy as a generalised ensemble average, replacing Gibbs-Boltzmann-Shannon's entropy definition enabling construction of new forms of statistical mechanics. The general entropy may also be of importance in information theory and data analysis. Application to generalised Lorentzian phase space elements yields the Gibbs-Lorentzian power law probability distribution and statistical mechanics. The corresponding Boltzmann, Fermi and Bose-Einstein distributions are found. They apply only to finite temperature states including correlations. As a by-product any negative absolute temperatures are categorically excluded, supporting a recent ``no-negative $T$ claim. |
topic |
Information Theory entropy Statistical Mechanics maximum entropy Generalised Lorentzian distributions |
url |
http://journal.frontiersin.org/Journal/10.3389/fphy.2014.00049/full |
work_keys_str_mv |
AT rudolfatreumann beyondgibbsboltzmannshannongeneralentropiesthegibbslorentzianexample AT wolfgangebaumjohann beyondgibbsboltzmannshannongeneralentropiesthegibbslorentzianexample |
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