Thermodynamic stability of asymptotically anti-de Sitter rotating black holes in higher dimensions

Conditions for thermodynamic stability of asymptotically anti-de Sitter rotating black holes in D-dimensions are determined. Local thermodynamic stability requires not only positivity conditions on the specific heat and the moment of inertia tensor but it is also necessary that the adiabatic compressibility be positive. It is shown that, in the absence of a cosmological constant, neither rotation nor charge is sufficient to ensure full local thermodynamic stability of a black hole. Thermodynamic stability properties of anti-de Sitter Myers-Perry black holes are investigated for both singly spinning and multi-spinning black holes. Simple expressions are obtained for the specific heat and moment of inertia tensor in any dimension. An analytic expression is obtained for the boundary of the region of parameter space in which such space-times are thermodynamically stable.Comment: 30 pages, 3 figures. References added, minor typos corrected in v

Measuring thermodynamic length

Thermodynamic length is a metric distance between equilibrium thermodynamic states. Among other interesting properties, this metric asymptotically bounds the dissipation induced by a finite time transformation of a thermodynamic system. It is also connected to the Jensen-Shannon divergence, Fisher information and Rao's entropy differential metric. Therefore, thermodynamic length is of central interest in understanding matter out-of-equilibrium. In this paper, we will consider how to define thermodynamic length for a small system described by equilibrium statistical mechanics and how to measure thermodynamic length within a computer simulation. Surprisingly, Bennett's classic acceptance ratio method for measuring free energy differences also measures thermodynamic length.Comment: 4 pages; Typos correcte

Thermodynamics of noncommutative quantum Kerr black holes

Thermodynamic formalism for rotating black holes, characterized by noncommutative and quantum corrections, is constructed. From a fundamental thermodynamic relation, equations of state and thermodynamic response functions are explicitly given and the effect of noncommutativity and quantum correction is discussed. It is shown that the well known divergence exhibited in specific heat is not removed by any of these corrections. However, regions of thermodynamic stability are affected by noncommutativity, increasing the available states for which some thermodynamic stability conditions are satisfied.Comment: 16 pages, 9 figure

Geometric description of BTZ black holes thermodynamics

We study the properties of the space of thermodynamic equilibrium states of the Ba\~nados-Teitelboim-Zanelli (BTZ) black hole in (2+1)-gravity. We use the formalism of geometrothermodynamics to introduce in the space of equilibrium states a $2-$dimensional thermodynamic metric whose curvature is non-vanishing, indicating the presence of thermodynamic interaction, and free of singularities, indicating the absence of phase transitions. Similar results are obtained for generalizations of the BTZ black hole which include a Chern-Simons term and a dilatonic field. Small logarithmic corrections of the entropy turn out to be represented by small corrections of the thermodynamic curvature, reinforcing the idea that thermodynamic curvature is a measure of thermodynamic interaction

Phase transitions in geometrothermodynamics

Using the formalism of geometrothermodynamics, we investigate the geometric properties of the equilibrium manifold for diverse thermodynamic systems. Starting from Legendre invariant metrics of the phase manifold, we derive thermodynamic metrics for the equilibrium manifold whose curvature becomes singular at those points where phase transitions of first and second order occur. We conclude that the thermodynamic curvature of the equilibrium manifold, as defined in geometrothermodynamics, can be used as a measure of thermodynamic interaction in diverse systems with two and three thermodynamic degrees of freedom

Quasi-Homogeneous Thermodynamics and Black Holes

We propose a generalized thermodynamics in which quasi-homogeneity of the thermodynamic potentials plays a fundamental role. This thermodynamic formalism arises from a generalization of the approach presented in paper [1], and it is based on the requirement that quasi-homogeneity is a non-trivial symmetry for the Pfaffian form $\delta Q_{rev}$. It is shown that quasi-homogeneous thermodynamics fits the thermodynamic features of at least some self-gravitating systems. We analyze how quasi-homogeneous thermodynamics is suggested by black hole thermodynamics. Then, some existing results involving self-gravitating systems are also shortly discussed in the light of this thermodynamic framework. The consequences of the lack of extensivity are also recalled. We show that generalized Gibbs-Duhem equations arise as a consequence of quasi-homogeneity of the thermodynamic potentials. An heuristic link between this generalized thermodynamic formalism and the thermodynamic limit is also discussed.Comment: 39 pages, uses RevteX. Published version (minor changes w.r.t. the original one