Non-unique way to generalize the Boltzmann-Gibbs distribution

TL;DR

This paper explores alternative definitions for core concepts in generalized thermostatistics, questioning some assumptions in Tsallis' nonextensive framework and proposing new perspectives on entropy and distribution generalizations.

Contribution

It introduces alternative formulations of entropy and distribution generalizations, challenging existing assumptions in Tsallis' nonextensive thermostatistics.

Findings

Proposes new definitions for generalized entropy and distributions.

Questions specific choices in Tsallis' framework.

Provides alternative perspectives on thermostatistical concepts.

Abstract

Alternative definitions are given of basic concepts of generalized thermostatistics. In particular, generalizations of Shannon's entropy, of the Boltzmann-Gibbs distribution, and of relative entropy are considered. Particular choices made in Tsallis' nonextensive thermostatistics are questioned.