Thermodynamic Consistency of the $q$-Deformed Fermi-Dirac Distribution in Nonextensive Thermostatics

TL;DR

This paper examines the thermodynamic consistency of the $q$-deformed Fermi-Dirac distribution in nonextensive thermostatistics, highlighting challenges and proposing methods for consistent application in quantum many-body systems.

Contribution

It identifies subtle issues in applying $q$-deformed fermion distributions and explores solutions for maintaining thermodynamic consistency.

Findings

Identifies difficulties in $q$-deformed distribution applications

Proposes methods for thermodynamic consistency

Highlights implications for quantum many-body systems

Abstract

The $q$-deformed statistics for fermions arising within the non-extensive thermostatistical formalism has been applied to the study of various quantum many-body systems recently. The aim of the present note is to point out some subtle difficulties presented by this approach in connection with the problem of thermodynamic consistency. Different possible ways to apply the $q$-deformed quantum distributions in a thermodynamically consistent way are considered.