Volume 48, Number 1, October I 1999
|Page(s)||8 - 14|
|Published online||01 September 2002|
Quantum-statistical mechanics in the Lorentzian domain
Max-Planck-Institute for extraterrestrial Physics P.O. Box 1603, D-85740 Garching, Germany International Space Science Institute - Hallerstr. 6, CH-3012 Bern, Switzerland
Accepted: 8 August 1999
A recently constructed generalised-Boltzmann statistical mechanics (a complement to the Daróczy-Tsallis "non-extensive” statistics) is extended into the quantum domain. We introduce a control parameter κ, postulate the generalised collision integral and derive the generalised Fermi-Dirac and Bose-Einstein distribution functions for quantum gases in equilibrium. The analogy to the Boltzmann case proves the validity of the thermodynamic relations. The grand thermodynamic potential assumes a complicated but suggestive form. The generalized Fermi gas has no real zero-temperature states. At it becomes the ordinary Fermi gas. This is interpreted as destruction of correlations as . The low-temperature dependence of the control parameter is determined.
PACS: 05.20.-y – Classical statistical mechanics / 05.30.-d – Quantum statistical mechanics
© EDP Sciences, 1999
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