A unified grand canonical description of the nonextensive thermostatistics of the quantum gases: Fractal and fractional approach
Department of Physics, Faculty of
Science, Ege University, 35100 Bornova-zmir, Turkey
Published online: 15 April 2000
In this paper, the particles of quantum gases, that is, bosons and fermions are regarded as g-ons which obey fractional exclusion statistics. With this point of departure the thermostatistical relations concerning the Bose and Fermi systems are unified under the g-on formulation where a fractal approach is adopted. The fractal inspired entropy, the partition function, distribution function, the thermodynamics potential and the total number of g-ons have been found for a grand canonical g-on system. It is shown that from the g-on formulation; by a suitable choice of the parameters of the nonextensivity q, the parameter of the fractional exclusion statistics g, nonextensive Tsallis (q≠1) as well as extensive (q=1) standard thermostatistical relations of the Bose and Fermi systems are recovered.
PACS: 05.20.-y – Classical statistical mechanics / 03.65.-w – Quantum mechanics
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000