Non-extensive statistics in free-electron metals and thermal effective mass

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.