Microscopic Foundation of Nonextensive Statistics

Details Microscopic Foundation of Nonextensive Statistics Microscopic Foundation of Nonextensive Statistics

1998-09-22

arxiv.org/abs/quant-ph/9809061v1

Phys.Rev. E59 (1999) 2497

Physics

Quantum Physics

revtex

Scientific paper

10.1103/PhysRevE.59.R2497

Combination of the Liouville equation with the q-averaged energy $U_q = _q$ 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 $F_q=U_q-TS_q$ 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 $q\neq 1$ the corresponding macroscopic dynamics is irreversible.

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