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

TL;DR

This paper extends Gibbs' statistical mechanics by introducing a generalized entropy framework that accounts for phase space correlations, leading to new probability distributions like the Gibbs-Lorentzian, with potential applications in physics and information theory.

Contribution

It develops a generalized entropy and probability distribution framework that extends classical Gibbs-Boltzmann-Shannon statistics to correlated systems, exemplified by the Gibbs-Lorentzian case.

Findings

Derived a generalized entropy suitable for correlated phase spaces

Established the Gibbs-Lorentzian power law distribution

Potential applications in information theory and data analysis

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. Details can be found in arXiv:1406.6639