Nonperturbative thermodynamic geometry of nonextensive statistics

Following our earlier work on the perturbative thermodynamic geometry of nonextensive quantum and classical gases [H. Mohammadzadeh, F. Adli and S. Nouri, Phys. Rev. E 94 (2016) 062118], we study [Formula: see text]-generalized Bose–Einstein, Fermi–Dirac and classical statistics nonperturbatively. We define [Formula: see text]-generalized polylogarithm functions and evaluate thermodynamics quantities such as internal energy and particle number. We construct the thermodynamic geometry of nonextensive Bose (Fermi) ideal gas and show that the thermodynamic curvature is positive(negative) in full physical range as the same as ordinary statistics. Also, we show that the thermodynamic geometry of nonextensive ideal classical gas is flat, similar to the ordinary one. Therefore, the nonextensive parameter does not change the nature of intrinsic statistical interactions. We argue that the nonextensive boson gas might be more stable than the boson gas due to conjectural interpretation of thermodynamic curvature. In the following, we extract the singular points of thermodynamic curvature of nonextensive Bose gas and relate it to the condensation. We evaluate some thermodynamic quantities such as heat capacities, compressibility and [Formula: see text]-dependent phase transition temperature. We show that the heat capacity is not differentiable at critical temperature, [Formula: see text] which is reduced by increasing nonextensive parameter [Formula: see text]. Moreover, the critical temperature and possibility of condensation is investigated for different values of nonextensive parameter in various dimensions.

Some New Transformation Properties of the Nielsen Generalized Polylogarithm

Many of the properties of Nielsen generalized polylogarithmSn,p(z), for example, the special value and the transformation formulas, play important roles in the computation of higher order radiative corrections in quantum electrodynamics. In this paper, some transformation formulas ofz→p(z),p(z)=1-z,1/z,1/(1-z),z/(z-1), and(1-z)/zare obtained. In particular, the last three transformation formulas are new results so far in the literature. By use of these transformation formulas presented, new fast algorithms for Nielsen generalized polylogarithmSn,p(z)can be designed. Forsn,p=Sn,p(1), a new recurrence formula is also given. The identities and the calculation ofσn,pandan,pare also investigated.