Issue |
Europhys. Lett.
Volume 48, Number 1, October I 1999
|
|
---|---|---|
Page(s) | 8 - 14 | |
Section | General | |
DOI | https://doi.org/10.1209/epl/i1999-00106-9 | |
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
Received:
11
January
1999
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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