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Microscopic Foundation of Nonextensive Statistics

Marek Czachor·Jan Naudts
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Abstract

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: $i\dotρ=[H,ρ^q]$. 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 $ρ$ is reversible for any q, but for $q\neq 1$ the corresponding macroscopic dynamics is irreversible.

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Marek Czachor, Jan Naudts. 1998-09-22. Microscopic Foundation of Nonextensive Statistics. https://doi.org/10.1103/physreve.59.r2497

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