Europhys. Lett.
Volume 48, Number 1, October 1999
Page(s) 8 - 14
Section General
Published online 01 September 2002
DOI: 10.1209/epl/i1999-00106-9

Europhys. Lett, 48 (1), pp. 8-14 (1999)

Quantum-statistical mechanics in the Lorentzian domain

R. A. Treumann

Max-Planck-Institute for extraterrestrial Physics
P.O. Box 1603, D-85740 Garching, Germany
International Space Science Institute - Hallerstr. 6, CH-3012 Bern, Switzerland

(received 11 January 1999; accepted in final form 8 August 1999)

PACS. 05.20-y - Classical statistical mechanics.
PACS. 05.30-d - Quantum statistical mechanics.


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 $\kappa$, 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 T=0 it becomes the ordinary Fermi gas. This is interpreted as destruction of correlations as $T\to 0$. The low-temperature dependence of the control parameter $\kappa(T)$ is determined.


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