Thermodynamics, stability and Hawking-Page transition of Kerr black holes from R\'enyi statistics

Thermodynamics of rotating black holes described by the R\'enyi formula as equilibrium and zeroth law compatible entropy function is investigated. We show that similarly to the standard Boltzmann approach, isolated Kerr black holes are stable with respect to axisymmetric perturbations in the R\'enyi model. On the other hand, when the black holes are surrounded by a bath of thermal radiation, slowly rotating black holes can also be in stable equilibrium with the heat bath at a fixed temperature, in contrast to the Boltzmann description. For the question of possible phase transitions in the system, we show that a Hawking-Page transition and a first order small black hole/large black hole transition occur, analogous to the picture of rotating black holes in AdS space. These results confirm the similarity between the R\'enyi-asymptotically flat and Boltzmann-AdS approaches to black hole thermodynamics in the rotating case as well. We derive the relations between the thermodynamic parameters based on this correspondence.Comment: 29 pages, 20 figure

Black hole horizons can hide positive heat capacity

Regarding the volume as independent thermodynamic variable we point out that black hole horizons can hide positive heat capacity and specific heat. Such horizons are mechanically marginal, but thermally stable. In the absence of a canonical volume definition, we consider various suggestions scaling differently with the horizon radius. Assuming Euler-homogeneity of the entropy, besides the Hawking temperature, a pressure and a corresponding work term render the equation of state at the horizon thermally stable for any meaningful volume concept that scales larger than the horizon area. When considering also a Stefan--Boltzmann radiation like equation of state at the horizon, only one possible solution emerges: the Christodoulou--Rovelli volume, scaling as $V\sim R^5$, with an entropy $S = \frac{8}{3}S_{BH}$.Comment: 5 pages, no figures, to be published in Phys. Lett.

Classical no-cloning theorem under Liouville dynamics by non-Csisz\'ar f-divergence

The Csisz\'ar f-divergence, which is a class of information distances, is known to offer a useful tool for analysing the classical counterpart of the cloning operations that are quantum mechanically impossible for the factorized and marginality classical probability distributions under Liouville dynamics. We show that a class of information distances that does not belong to this divergence class also allows for the formulation of a classical analogue of the quantum no-cloning theorem. We address a family of nonlinear Liouville-like equations, and generic distances, to obtain constraints on the corresponding functional forms, associated with the formulation of classical analogue of the no-cloning principle.Comment: 6 pages, revised, published versio

Physical aspects of naked singularity explosion - How does a naked singularity explode? --

The behaviors of quantum stress tensor for the scalar field on the classical background of spherical dust collapse is studied. In the previous works diverging flux of quantum radiation was predicted. We use the exact expressions in a 2D model formulated by Barve et al. Our present results show that the back reaction does not become important during the semiclassical phase. The appearance of the naked singularity would not be affected by this quantum field radiation. To predict whether the naked singularity explosion occurs or not we need the theory of quantum gravity. We depict the generation of the diverging flux inside the collapsing star. The quantum energy is gathered around the center positively. This would be converted to the diverging flux along the Cauchy horizon. The ingoing negative flux crosses the Cauchy horizon. The intensity of it is divergent only at the central naked singularity. This diverging negative ingoing flux is balanced with the outgoing positive diverging flux which propagates along the Cauchy horizon. After the replacement of the naked singularity to the practical high density region the instantaneous diverging radiation would change to more milder one with finite duration.Comment: 18 pages, 16 figure

Topological Origin of Zero-Energy Edge States in Particle-Hole Symmetric Systems

A criterion to determine the existence of zero-energy edge states is discussed for a class of particle-hole symmetric Hamiltonians. A ``loop'' in a parameter space is assigned for each one-dimensional bulk Hamiltonian, and its topological properties, combined with the chiral symmetry, play an essential role. It provides a unified framework to discuss zero-energy edge modes for several systems such as fully gapped superconductors, two-dimensional d-wave superconductors, and graphite ribbons. A variants of the Peierls instability caused by the presence of edges is also discussed.Comment: Completely rewritten. Discussions on coexistence of is- or id_{xy}-wave order parameter near edges in d_{x^{2}-y^{2}}-wave superconductors are added; 4 pages, 3 figure

Thermodynamics of ideal quantum gas with fractional statistics in D dimensions

We present exact and explicit results for the thermodynamic properties (isochores, isotherms, isobars, response functions, velocity of sound) of a quantum gas in dimensions D>=1 and with fractional exclusion statistics 0<=g<=1 connecting bosons (g=0) and fermions (g=1). In D=1 the results are equivalent to those of the Calogero-Sutherland model. Emphasis is given to the crossover between boson-like and fermion-like features, caused by aspects of the statistical interaction that mimic long-range attraction and short-range repulsion. The full isochoric heat capacity and the leading low-T term of the isobaric expansivity in D=2 are independent of g. The onset of Bose-Einstein condensation along the isobar occurs at a nonzero transition temperature in all dimensions. The T-dependence of the velocity of sound is in simple relation to isochores and isobars. The effects of soft container walls are accounted for rigorously for the case of a pure power-law potential.Comment: 15 pages, 31 figure

Magnetized configurations with black holes and Kaluza-Klein bubbles: Smarr-like relations and first law

We present a general class of exact solutions in Einstein-Maxwell-dilaton gravity describing configurations of black holes and Kaluza-Klein bubbles magnetized along the compact dimension. Smarr-like relations for the mass and the tension are found. We also derive the mass and tension first law for the configurations under consideration using the Noether current approach. The solutions we consider are explicit examples showing that in Kaluza-Klein spacetimes the interval (rod) structure and the charges (which are zero by construction for the solutions here), are insufficient to classify the solutions and additional data is necessary, namely the magnetic flux(es).Comment: 13 page

Thermoelectric Polarization Transport in Ferroelectric Ballistic Point Contacts

We formulate a scattering theory of polarization and heat transport through a ballistic ferroelectric point contact. We predict a polarization current under either an electric field or a temperature difference that depends strongly on the direction of the ferroelectric order and can be detected by its magnetic stray field and associated thermovoltage and Peltier effect