Thermodynamic Geometry of Normal (Exotic) BTZ Black Hole Regarding to the Fluctuation of Cosmological Constant

We construct the thermodynamic geometry of ([Formula: see text])-dimensional normal (exotic) BTZ black hole regarding the fluctuation of cosmological constant. We argue that while the thermodynamic geometry of black hole without fluctuation of cosmological constant is a two dimensional flat space, the three-dimensional space of thermodynamics parameters including the cosmological constant as a fluctuating parameter is curved. Some consequences of the fluctuation of cosmological constant will be investigated. We show that such a fluctuation leads to a thermodynamic curvature which is singular at the critical surface. Also, we consider the validity of first thermodynamics law regarding the fluctuation of the cosmological constant.

Thermodynamic Curvature of the Binary van der Waals Fluid

The thermodynamic Ricci curvature scalar R has been applied in a number of contexts, mostly for systems characterized by 2D thermodynamic geometries. Calculations of R in thermodynamic geometries of dimension three or greater have been very few, especially in the fluid regime. In this paper, we calculate R for two examples involving binary fluid mixtures: a binary mixture of a van der Waals (vdW) fluid with only repulsive interactions, and a binary vdW mixture with attractive interactions added. In both of these examples, we evaluate R for full 3D thermodynamic geometries. Our finding is that basic physical patterns found for R in the pure fluid are reproduced to a large extent for the binary fluid.

Diagnosis inspired by the thermodynamic geometry for different thermodynamic schemes of the charged BTZ black hole

Due to the asymptotic structure of the black hole solution, there are two different thermodynamic schemes for the charged Banados–Teitelboim–Zanelli (BTZ) black hole. In one scheme, the charged BTZ black hole is super-entropic, while in the other, it is not (the reverse isoperimetric inequality is saturated). In this paper, we investigate the thermodynamic curvature of the charged BTZ black hole in different coordinate spaces. We find that in both schemes, the thermodynamic curvature is always positive, which may be related to the information of repulsive interaction between black hole molecules for the charged BTZ black hole if we accept an empirical relationship between the thermodynamic curvature and interaction of a system. More importantly, we provide a diagnosis for the discrimination of the two schemes from the point of view of the thermodynamics geometry. For the charged BTZ black hole, when the reverse isoperimetric inequality is saturated, the thermodynamic curvature of an extreme black hole tends to be infinity, while when the reverse isoperimetric inequality is violated, the thermodynamic curvature of the extreme black hole goes to a finite value.

Some information from thermodynamic curvature of Chaplygin gas

In this paper, we study thermodynamic curvature of Chaplygin gas which is one of the dark energy candidates in terms of entropy and temperature. So, we get some information about past universe by considering thermodynamic curvature of Chaplygin gas. In addition to thermodynamic curvature, we study behaviors of test particle in the universe filled with Chaplygin gas.

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.