Phys. Rev. E 59, R2497–R2500 (1999)Microscopic foundation of nonextensive statistics
A combination of the Lie-Poisson equation with the q-averaged energy Uq=〈H〉q leads to a microscopic framework for nonextensive q thermodynamics. The resulting von Neumann equation is nonlinear: iρ̇=[H,ρq]. In spite of its nonlinearity the dynamics is consistent with linear quantum mechanics of pure states. The free energy Fq=Uq-TSq is a stability function for the dynamics. This implies that q-equilibrium states are dynamically stable. The (microscopic) evolution of ρ is reversible for any q, but for q≠1 the corresponding macroscopic dynamics is irreversible. © 1999 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.59.R2497
DOI:
10.1103/PhysRevE.59.R2497
PACS:
05.20.-y, 05.30.-d, 05.70.Ln
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