Non-Extensive Statistics in Free-Electron Metals and Thermal Effective Mass

TL;DR

This paper applies non-extensive Tsallis statistics to free-electron metals to accurately model their electronic specific heat and effective mass, revealing a systematic dependence on the non-extensive parameter q.

Contribution

It introduces a non-extensive statistical approach to describe electron behavior in metals, extending traditional models with the q-exponential function.

Findings

Non-extensive parameter q is typically greater than 1 for metals.

The effective mass ratio m*/m depends systematically on q.

Tsallis statistics effectively describe electrons with long-range correlations.

Abstract

We have applied the non-extensive statistical mechanics to free electrons in several metals to calculate the electronic specific heat at low temperature. In this case, the Fermi-Dirac (FD) function is modified from its Boltzmann-Gibbs (BG) form, with the exponential part going to a $q$-exponential, in its non-extensive form. In most cases, the non-extensive parameter, $q$, is found to be greater than unity to produce the correct thermal effective mass, $m^*$, of electrons. The ratio $m^*/m$ is found to show a nice systematic dependence on $q$. Results indicate, electrons in metals, in the presence of long range correlations are reasonably well described by Tsallis statistics.