Essential discreteness in generalized thermostatistics with non-logarithmic entropy

TL;DR

This paper argues that for generalized thermostatistics with non-logarithmic entropy to be thermodynamically valid, the basic physical variables must be discrete, excluding continuous systems like those with q-Gaussian distributions.

Contribution

It demonstrates that discreteness is essential for the thermodynamic applicability of non-logarithmic entropy-based statistical mechanics.

Findings

Discreteness of variables is necessary for generalized thermostatistics.

Continuous Hamiltonian systems with long-range interactions are outside its scope.

q-Gaussian distributions are incompatible with this framework.

Abstract

It is shown by simple and straightforward considerations that discreteness of basic physical variables is, at least, essential for generalized statistical mechanics with non-logarithmic entropy to be thermodynamically applicable to classical systems. As a result, continuous Hamiltonian systems with long-range interactions and the so-called q-Gaussian momentum distributions are seen to be outside the scope of nonextensive statistical mechanics.