Density matrix for a consistent non-extensive thermodynamics

TL;DR

This paper derives density matrices and Hamiltonians for non-extensive thermodynamics, revealing deformed algebra and interaction terms, and introduces a nonlinear equation with a two-parameter solution linked to anomalous diffusion.

Contribution

It provides a novel formulation of density matrices for non-extensive thermodynamics, including deformed algebra and a nonlinear equation with a two-parameter solution.

Findings

Deformed bosonic algebra in the density matrix

Hamiltonian with interaction terms in powers of number operators

Nonlinear equation with a two-parameter solution related to anomalous diffusion

Abstract

Starting with the average particle distribution function for bosons and fermions for non-extensive thermodynamics , as proposed in \cite{CMP}, we obtain the corresponding density matrix operators and hamiltonians. In particular, for the bosonic case the corresponding operators satisfy a deformed bosonic algebra and the hamiltonian involves interacting terms in powers of $a^{\dagger}_ja_j$ standard creation and annihilation operators. For the unnormalized density matrix we obtain a nonlinear equation that leads to a two-parameter solution relevant to anomalous diffusion phenomena.