V. Pineda-Reyes

TL;DR: This work considers the alternative statistical framework of Tsallis and analyzes the statistical and thermodynamical implications for a self-gravitating gas, obtaining analytical and convergent expressions for the equation of state and specific heat in the ensembles of constant temperature and constant energy.

TL;DR: In this paper, it was shown that these metrics also have a statistical origin which can be expressed in terms of the average and variance of the differential of the microscopic entropy, and a particular reparametrization of the coordinates of the corresponding thermodynamic phase space was used to show this.

TL;DR: In this article, it was shown that a Legendre transformation is a mere change of contact polarization from the point of view of contact geometry and that it is not possible to find a class of metric tensors which fulfills two properties: on the one hand, to be polarization independent i.e. the Legendre transformations are the corresponding isometries and, on the other, that it induces a Hessian metric into the corresponding Legendre submanifolds.

TL;DR: In this paper, the consequences of reparametrizations in the geometric description of thermodynamics analyzing the effects on the thermodynamic phase space are investigated. But the authors do not consider a set of differentiable functions of the extensive variables accounting for the possibility of not having direct access to the original variables.

TL;DR: In this paper, it was shown that a Legendre transformation is a mere change of symplectic polarization from the point of view of contact geometry and it is not possible to find a class of metric tensors which fulfills two properties: on the one hand, to be polarization independent, and on the other, to induce a Hessian metric into the corresponding Legendre submanifolds.