Nonextensive statistical mechanics of q-bosons based on the q-deformed entropy

Jack A. Tuszyński, Jacques L. Rubin, J. Meyer +1 more

Rinat G. Zaripov

Rinat G. Zaripov

Luca Salasnich

We discuss the Bose-Einstein condensation (BEC) for an ideal gas of bosons in the framework of Tsallis’s nonextensive statistical mechanics. We study the corrections to the standard BEC formulas due to a weak nonextensivity of the system. In particular, we consider three cases in the D-dimensional space: the homogeneous gas, the gas in a harmonic trap and the relativistic homogenous gas. The results show that small deviations from the extensive Bose statistics produce remarkably large changes in the BEC transition temperature. PACS numbers: 05.30-d; 03.75.Fi 1 A decade ago, Tsallis introduced a nonextensive statistical mechanics (NSM) to describe systems for which the additivity property of entropy does not hold. 1 The NSM can describe systems for which long-range microscopic memory, fractal space-time constraints or long-range interactions affect the thermalization process. 2 The NSM is characterized by a parameter q such

T. K. Kopeć

Hiroshi Hasegawa

It is shown by way of examples that the quantum correspondent to Fisher information in statistics named quantum information metric is an extensive quantity in spite of the nonextensivity of the quantum q-deformed relative entropy. A general proof is presented, and some related topics on the quantum relative entropies vs the metrics are discussed.