Related papers: Critical phenomena and information geometry in bla…
The Ruppeiner metric as determined by the Hessian of the Gibbs surface provides a geometric description of thermodynamic systems in equilibrium. An interesting example is a black hole in equilibrium with its own Hawking radiation. In this…
The Hessian of the entropy function can be thought of as a metric tensor on state space. In the context of thermodynamical fluctuation theory Ruppeiner has argued that the Riemannian geometry of this metric gives insight into the underlying…
In this paper, we examine the thermodynamic geometry of four-dimensional quasi-topological black holes by computing the Ruppeiner scalar curvature R which serves as an empirical tool to describe the nature of interactions among black hole…
Thermodynamic fluctuation metrics in Ruppeiner's formalism are worked out for Kerr-AdS black holes in the extended state space. The implications of constraints upon the state space geometry and their correspondence with thermodynamical…
This paper studies the thermodynamics and Ruppeiner geometry of D-dimensional RN black holes. We analyze the thermodynamic curvature scalar $R$ in various thermodynamic ensembles. It is found that in an ensemble of fixed charge (canonical…
The geometry of thermodynamic state space is studied for asymptotically anti-de Sitter black holes in D-dimensional space times. Convexity of thermodynamic potentials and the analytic structure of the response functions is analysed. The…
In some recent studies \cite{aman1, aman2, aman3}, Aman {\it et al.} used the Ruppeiner scalar as a measure of underlying interactions of Reissner-Nordstr\"{o}m black holes, indicating that it is a non-interacting statistical system for…
We study thermodynamic properties of Myers-Perry black holes by deriving explicit fundamental relations from which we can obtain the temperature and specific heat in terms of explicit control parameters in arbitrary dimensions. Using the…
The application of information geometric ideas to statistical mechanics using a metric on the space of states, pioneered by Ruppeiner and Weinhold, has proved to be a useful alternative approach to characterizing phase transitions. Some…
We consider the thermodynamics and Geometrothermodynamics of the Myers-Perry black holes in five dimensions for three different cases, depending on the values of the angular momenta. We follow Davies approach to study the thermodynamics of…
Based on the observations that there exists an analogy between the Reissner-Nordstr\"om-anti-de Sitter (RN-AdS) black holes and the van der Waals-Maxwell liquid-gas system, in which a correspondence of variables is $(\phi, q)…
The thermodynamics of black holes is reformulated within the context of the recently developed formalism of geometrothermodynamics. This reformulation is shown to be invariant with respect to Legendre transformations, and to allow several…
Thermodynamics unavoidably contains fluctuation theory, expressible in terms of a unique thermodynamic information metric. This metric produces an invariant thermodynamic Riemannian curvature scalar $R$ which, in fluid and spin systems,…
Geometrical properties of the extreme Kerr black holes in the topological sectors of nonextreme and extreme configurations are studied. We find that the Euler characteristic plays an essential role to distinguish these two kinds of extreme…
We study thermodynamical structure of Einstein black holes in the presence of power Maxwell invariant nonlinear electrodynamics for two different cases. The behavior of the temperature and conditions regarding the stability of these black…
The Hessian of the entropy function can be thought of as a metric tensor on the state space. In the context of thermodynamical fluctuation theory Ruppeiner has argued that the Riemannian geometry of this metric gives insight into the…
In this paper we show that the vanishing of the scalar curvature of Ruppeiner-like metrics does not characterize the ideal gas. Furthermore, we claim through an example that flatness is not a sufficient condition to establish the absence of…
A coordinate system that blockwise-simplifies the Kerr-Newman black hole's thermodynamical state space Ruppeiner metric geometry is constructed, with discussion of the limiting cases corresponding to simpler black holes. It is deduced that…
We resolve the controversial issue of the geometric approach to the black hole thermodynamics. The geometric description of the equilibrium thermodynamics comes from Ruppeiner geometry based on a metric on the thermodynamic state space. For…
Combining with the small-large black hole phase transition, the thermodynamic geometry has been well applied to study the microstructure for the charged AdS black hole. In this paper, we extend the geometric approach to the rotating…