On the Cut-Off Prescriptions Associated with Power-Law Generalized Thermostatistics

TL;DR

This paper proposes an alternative cut-off prescription for Tsallis' maximum entropy distributions for q>1, exploring its mathematical properties and applying it to q-generalized quantum distributions relevant to high-temperature superconductors.

Contribution

It introduces a new cut-off prescription for Tsallis distributions and analyzes its mathematical properties and applications to quantum systems.

Findings

New cut-off prescription for q>1 in Tsallis distributions

Mathematical properties of the proposed cut-off

Application to high T_c superconductor models

Abstract

We revisit the cut-off prescriptions which are needed in order to specify completely the form of Tsallis' maximum entropy distributions. For values of the Tsallis entropic parameter $q>1$ we advance an alternative cut-off prescription and discuss some of its basic mathematical properties. As an illustration of the new cut-off prescription we consider in some detail the $q$-generalized quantum distributions which have recently been shown to reproduce various experimental results related to high $T_c$ superconductors.