Kaniadakis statistics and the quantum \(H\)-theorem. (English) Zbl 1241.82011
Summary: A proof of the quantum \(H\)-theorem in the context of Kaniadakis’ entropy concept \(S_{\kappa}^Q\) and a generalization of stosszahlansatz are presented, showing that there exists a quantum version of the second law of thermodynamics consistent with the Kaniadakis statistics. It is also shown that the marginal equilibrium states are described by quantum \(\kappa \)-power law extensions of the Fermi-Dirac and Bose-Einstein distributions.
MSC:
| 82B05 | Classical equilibrium statistical mechanics (general) |
| 82B10 | Quantum equilibrium statistical mechanics (general) |
| 82B30 | Statistical thermodynamics |
| 82B31 | Stochastic methods applied to problems in equilibrium statistical mechanics |
| 82B40 | Kinetic theory of gases in equilibrium statistical mechanics |
| 94A17 | Measures of information, entropy |
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