Foundations of Nonextensive Statistical Mechanics and Its Cosmological Applications

Details Foundations of Nonextensive Statistical Mechanics and Its Cosmological Applications Foundations of Nonextensive Statistical Mechanics and Its Cosmological Applications

Apr 2004

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004ap%26ss.290..275p&link_type=abstract

Astrophysics and Space Science, v. 290, Issue 3, p. 275-286 (2004).

Physics

Condensed Matter

Statistical Mechanics

8

Nonextensive Statistical Mechanics, Quantum Distributions, Cosmology

Scientific paper

The q-generalized quantum distributions, arising within the context of q-nonextensive thermostatistics, have recently found interesting applications to cosmology. These applications rest upon an approximated form of the q-distributions whose properties are not yet completely known. In order to shed some new light on this subject we consider here a maximum entropy principle leading to the q-generalized Fermi Dirac distribution. This variational principle is formulated entirely in terms of the mean occupation numbers. It constitutes a natural generalization to the nonextensive regime of the well-known prescription leading, in the standard q= 1 case, to the usual distribution for fermions. We analyze some important properties of this variational approach. In particular, we discuss 1) the invariance of the associated solutions under uniform shifts of the energy spectrum; 2) the role played by different kinds of constraints (i.e. linear or q-generalized constraints); and 3) the probabilistic interpretation of the variational procedure. The possibility of extending the present approach to bosons is also considered.

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