Thermodynamic consistency of the q-deformed Fermi–Dirac distribution in nonextensive thermostatics

Abstract

The q-deformed statistics for fermions arising within the nonextensive thermostatistical formalism has been applied to the study of various quantum many-body systems recently. The aimof 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 theq-deformed quantum distributions in a thermodynamically consistent way are considered.