dorsal/arxiv
View SchemaMicroscopic Foundation of Nonextensive Statistics
| Authors | Marek Czachor, Jan Naudts |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9809061 |
| URL | https://arxiv.org/abs/quant-ph/9809061 |
| DOI | 10.1103/PhysRevE.59.R2497 |
| Journal | Phys.Rev. E59 (1999) 2497 |
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 $F_q=U_q-TS_q$ 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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"abstract": "Combination of the Liouville equation with the q-averaged energy $U_q =\n\u003cH\u003e_q$ leads to a microscopic framework for nonextensive q-thermodynamics. The\nresulting von Neumann equation is nonlinear: $i\\dot\\rho=[H,\\rho^q]$. In spite\nof its nonlinearity the dynamics is consistent with linear quantum mechanics of\npure states. The free energy $F_q=U_q-TS_q$ is a stability function for the\ndynamics. This implies that q-equilibrium states are dynamically stable. The\n(microscopic) evolution of $\\rho$ is reversible for any q, but for $q\\neq 1$\nthe corresponding macroscopic dynamics is irreversible.",
"arxiv_id": "quant-ph/9809061",
"authors": [
"Marek Czachor",
"Jan Naudts"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevE.59.R2497",
"journal_ref": "Phys.Rev. E59 (1999) 2497",
"title": "Microscopic Foundation of Nonextensive Statistics",
"url": "https://arxiv.org/abs/quant-ph/9809061"
},
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