"Gibbsian" Approach to Statistical Mechanics yielding Power Law Distributions

TL;DR

This paper extends Gibbsian statistical mechanics to correlated systems, deriving new distributions that exhibit power-law behavior and challenge traditional quantum and temperature assumptions.

Contribution

It introduces a generalized Gibbsian framework for correlated systems, deriving distributions that produce power-law behaviors and exclude negative temperatures.

Findings

Derived Gibbsian distributions for correlated systems.

Showed quantum properties like Bose-Einstein condensation are lost.

Excluded negative absolute temperatures in the new framework.

Abstract

Gibbsian statistical mechanics is extended into the domain of non-negligible {though non-specified} correlations in phase space while respecting the fundamental laws of thermodynamics. The appropriate Gibbsian probability distribution is derived and the physical temperature identified. Consistent expressions for the canonical partition function are given. In a first application, the corresponding Boltzmann, Fermi and Bose-Einstein distributions are obtained. It is shown that the latter lose their typical quantum properties, i.e. the degenerate Fermi state and Bose-Einstein condensation. These distributions apply only to states at finite temperature with correlations. As a by-product these results \emph{exclude any negative absolute temperatures} also in the Boltzmann limit.