Microscopic Foundation of Nonextensive Statistics

Abstract

Combination of the Liouville equation with the q-averaged energy $U_q=<H{>}_q$ leads to a microscopic framework for nonextensive q-thermodynamics. The resulting von Neumann equation is nonlinear: $i\dot{\rho }=[H,{\rho }^q]$. In spite of its nonlinearity the dynamics is consistent with linear quantum mechanics of pure states. The free energy $F_q=U_q-T{S}_q$ is a stability function for the dynamics. This implies that q-equilibrium states are dynamically stable. The (microscopic) evolution of $\rho$ is reversible for any q, but for $q\ne 1$ the corresponding macroscopic dynamics is irreversible.

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References in corpus (5)

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