We obtain an analytic expression for the specific heat of a system of N rigid rotators exactly in the high temperature limit, and via a pertubative approach in the low temperature limit. We then evaluate the specific heat of a diatomic gas with both translational and rotational degrees of freedom, and conclude that there is a mixing between the translational and rotational degrees of freedom in nonextensive statistics.Comment: 12 page

a b s t r a c tInvestigating the canonical ensemble of a classical relativistic ideal gas in the Tsallis nonextensive framework we evaluate the specific heat in the extreme relativistic case in a closed form by directly employing the third constraint scenario. The canonical ensemble of N particles in D dimensions is well defined for the choice of the deformation parameter in the range 0 < q < 1 + 1 DN . In the instance of a classical relativistic ideal gas with arbitrarily massive particles a perturbative scheme in the nonextensivity parameter (1−q)is developed by employing an infinite product expansion of the q-exponential, and a direct transformation of the internal energy from the second to the third constraint picture. All thermodynamic quantities may be uniformly evaluated to any desired perturbative order.

We obtain a closed form expression of the universal T-matrix encapsulating the duality between the quantum superalgebra U q ͓osp͑1/2͔͒ and the corresponding supergroup OSp q ͑1/2͒. The classical q → 1 limit of this universal T-matrix yields the group element of the undeformed OSp q ͑1/2͒ supergroup. The finite dimensional representations of the quantum supergroup OSp q ͑1/2͒ are readily constructed employing the above-mentioned universal T-matrix and the known finite dimensional representations of the dually related deformed U q ͓osp͑1/2͔͒ superalgebra. Proceeding further, we derive the product law, the recurrence relations, and the orthogonality of the representations of the quantum supergroup OSp q ͑1/2͒. It is shown that the entries of these representation matrices are expressed in terms of the little Q-Jacobi polynomials with Q =−q. Two mutually complementary singular maps of the universal T-matrix on the universal R-matrix are also presented.

Using a realization of the q-exponential function as an infinite multiplicative series of the ordinary exponential functions we obtain new nonlinear connection formulae of the q-orthogonal polynomials such as q-Hermite, q-Laguerre and q-Gegenbauer polynomials in terms of their respective classical analogs.

A comprehensive investigation is carried out on the class of energy based ensembles. The eight ensembles are divided into two main classes. In the isothermal class of ensembles the individual members are at the same temperature. A unified framework is evolved to describe the four isothermal ensembles. Such a description is provided both in the second and the third constraint formalisms. The isothermalisobaric, grandcanonical and the generalized ensembles are illustrated through a study of the classical nonrelativistic and the extreme relativistic ideal gas models. In the adiabatic class of ensembles the individual members of the ensemble have the same value of the heat function and a unified formulation to described all the four ensembles is given. The nonrelativistic and the extreme relativistic ideal gases are studied in the isoenthalpic-isobaric ensemble, the adiabatic ensemble with number fluctuations, and, the adiabatic ensemble with number and particle fluctuations. PACS Number(s): 05.20.-y, 05.70