Non-Extensive Quantum Statistics with Particle - Hole Symmetry

TL;DR

This paper develops a symmetric non-extensive quantum statistical framework based on Tsallis entropy, addressing the challenge of maintaining particle-hole symmetry and smoothness at the Fermi level, which previous models failed to do.

Contribution

It introduces a novel ansatz dividing the deformed exponential into odd and even parts to ensure symmetry and smoothness, improving upon earlier approaches like kappa- and q-exponentials.

Findings

The proposed ansatz maintains particle-hole symmetry.

It ensures smooth behavior at the Fermi level.

It clarifies the behavior of earlier exponential deformations.

Abstract

Based on Tsallis entropy and the corresponding deformed exponential function, generalized distribution functions for bosons and fermions have been used since a while. However, aiming at a non-extensive quantum statistics further requirements arise from the symmetric handling of particles and holes (excitations above and below the Fermi level). Naive replacements of the exponential function or cut and paste solutions fail to satisfy this symmetry and to be smooth at the Fermi level at the same time. We solve this problem by a general ansatz dividing the deformed exponential to odd and even terms and demonstrate that how earlier suggestions, like the kappa- and q-exponential behave in this respect.