Beyond Gibbs-Boltzmann-Shannon: general entropies—the Gibbs-Lorentzian example

Frontiers in Physics

Treumann, Rudolf A.¹  Baumjohann, Wolfgang² 

[1] Geophysics Department, Munich University, Munich, Germany;International Space Science Institute, Bern, Switzerland

关键词: Statistical Mechanics;    entropy;    Generalised Lorentzian distributions;    Information Theory;    maximum entropy;   

DOI  :  10.3389/fphy.2014.00049

学科分类：物理（综合）

来源: Frontiers

【 摘 要 】

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.

【 授权许可】

CC BY