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Beyond Gibbs-Boltzmann-Shannon: General Entropies -- The Gibbs-Lorentzian Example

Treumann, R. A., and W. Baumjohann (2014), Beyond Gibbs-Boltzmann-Shannon: General Entropies -- The Gibbs-Lorentzian Example, Frontiers in Physics, 2(49), doi:10.3389/fphy.2014.00049, Perspective article, 5 Journal pages, slightly modified version available from arXiv under URL: http://arxiv.org/abs/1409.1719, OPEN ACCESS.

Abstract
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.
Further information
BibTeX
@article{id2019,
  author = {R. A. Treumann and W. Baumjohann},
  journal = {Frontiers in Physics},
  month = {aug},
  note = {Perspective article, 5 Journal pages, slightly modified version available from arXiv under URL: http://arxiv.org/abs/1409.1719, OPEN ACCESS},
  number = {49},
  title = {{Beyond Gibbs-Boltzmann-Shannon: General Entropies -- The Gibbs-Lorentzian Example}},
  volume = {2},
  year = {2014},
  url = {http://arxiv.org/abs/1409.1719},
  doi = {10.3389/fphy.2014.00049},
}
EndNote
%0 Journal Article
%A Treumann, R. A.
%A Baumjohann, W.
%D 2014
%N 49
%V 2
%J Frontiers in Physics
%Z Perspective article, 5 Journal pages, slightly modified version available from arXiv under URL: http://arxiv.org/abs/1409.1719, OPEN ACCESS
%T Beyond Gibbs-Boltzmann-Shannon: General Entropies -- The Gibbs-Lorentzian Example
%U http://arxiv.org/abs/1409.1719
%8 aug
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Printed 15. Dec 2019 22:13