1210.5499 (R. Chandrashekar et al.)

Adiabatic thermostatistics of the two parameter entropy and the role of
Lambert's W-function in its applications    [PDF]

R. Chandrashekar, J. Segar

The adiabatic class of ensembles corresponding to the generalized statistical mechanics based on the Schwammle-Tsallis two parameter (q, q^{\prime}) entropy is studied. A collective description of all the four adiabatic ensembles is provided. The generalized form of the equipartition theorem and the virial theorem are derived. The four adiabatic ensembles are individually illustrated using the classical nonrelativistic ideal gas. In the large N limit we find that the heat functions can be expressed in terms of the principal branch of the Lambert's W-function. The specific heat obtained from the heat functions was found to admit both positive and negative values depending on the choice of the deformation parameters. The effect of gravitational field on nonrelativistic classical ideal gas and a one dimensional system of hard rods confined in a finite region of space is studied in the microcanonical ensemble. In the infinite height limit, the internal energy and the specific heat of both the systems are again obtained in terms of the Lambert's W-function.

View original: http://arxiv.org/abs/1210.5499