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

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

arXiv comment6 pages, no figures, paper appeared in slightly different form in. For details on application see arXiv:1406.6639

References in corpus (5)

• Inconsistent thermostatistics and negative absolute temperatures
• Generalised-Lorentzian Thermodynamics
• Gibbsian theory of power law distributions
• Superdiffusion revisited in view of collisionless reconnection
• "Gibbsian" Approach to Statistical Mechanics yielding Power Law Distributions

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