Generalized thermostatistics based on deformed exponential and logarithmic functions

TL;DR

This paper generalizes thermostatistics by replacing the exponential function with a deformed exponential, unifying various approaches including Tsallis' thermostatistics through a formalism based on deformed functions.

Contribution

It introduces a generalized formalism of thermostatistics using deformed exponential and logarithmic functions, encompassing Tsallis' approach as a special case.

Findings

Derivation of a generalized equipartition theorem

Identification of Tsallis' thermostatistics as a specific instance

Establishment of a formal link between deformed functions and equilibrium distributions

Abstract

The equipartition theorem states that inverse temperature equals the log-derivative of the density of states. This relation can be generalized by introducing a proportionality factor involving an increasing positive function phi(x). It is shown that this assumption leads to an equilibrium distribution of the Boltzmann-Gibbs form with the exponential function replaced by a deformed exponential function. In this way one obtains a formalism of generalized thermostatistics introduced previously by the author. It is shown that Tsallis' thermostatistics, with a slight modification, is the most obvious example of this formalism and corresponds with the choice phi(x)=x^q.