New Types of Thermodynamics from (1+1)(1+1)-Dimensional Black Holes

For normal thermodynamic systems superadditivity $\S$, homogeneity \H and concavity \C of the entropy hold, whereas for $(3+1)$-dimensional black holes the latter two properties are violated. We show that $(1+1)$-dimensional black holes exhibit qualitatively new types of thermodynamic behaviour, discussed here for the first time, in which \C always holds, \H is always violated and $\S$ may or may not be violated, depending of the magnitude of the black hole mass. Hence it is now seen that neither superadditivity nor concavity encapsulate the meaning of the second law in all situations.Comment: WATPHYS-TH93/05, Latex, 10 pgs. 1 figure (available on request), to appear in Class. Quant. Gra

Gedanken experiments on nearly extremal black holes and the Third Law

A gedanken experiment in which a black hole is pushed to spin at its maximal rate by tossing into it a test body is considered. After demonstrating that this is kinematically possible for a test body made of reasonable matter, we focus on its implications for black hole thermodynamics and the apparent violation of the third law (unattainability of the extremal black hole). We argue that this is not an actual violation, due to subtleties in the absorption process of the test body by the black hole, which are not captured by the purely kinematic considerations.Comment: v2: minor edits, references added; v3: minor edits to match published versio

On the ideals of equivariant tree models

We introduce equivariant tree models in algebraic statistics, which unify and generalise existing tree models such as the general Markov model, the strand symmetric model, and group based models. We focus on the ideals of such models. We show how the ideals for general trees can be determined from the ideals for stars. The main novelty is our proof that this procedure yields the entire ideal, not just an ideal defining the model set-theoretically. A corollary of theoretical importance is that the ideal for a general tree is generated by the ideals of its flattenings at vertices.Comment: 23 pages. Greatly improved exposition, in part following suggestions by a referee--thanks! Also added exampl

Universal restrictions to the conversion of heat into work derived from the analysis of the Nernst theorem as a uniform limit

We revisit the relationship between the Nernst theorem and the Kelvin-Planck statement of the second law. We propose that the exchange of entropy uniformly vanishes as the temperature goes to zero. The analysis of this assumption shows that is equivalent to the fact that the compensation of a Carnot engine scales with the absorbed heat so that the Nernst theorem should be embedded in the statement of the second law. ----- Se analiza la relaci{\'o}n entre el teorema de Nernst y el enunciado de Kelvin-Planck del segundo principio de la termodin{\'a}mica. Se{\~n}alamos el hecho de que el cambio de entrop{\'\i}a tiende uniformemente a cero cuando la temperatura tiende a cero. El an{\'a}lisis de esta hip{\'o}tesis muestra que es equivalente al hecho de que la compensaci{\'o}n de una m{\'a}quina de Carnot escala con el calor absorbido del foco caliente, de forma que el teorema de Nernst puede derivarse del enunciado del segundo principio.Comment: 8pp, 4 ff. Original in english. Also available translation into spanish. Twocolumn format. RevTe

A tour on Hermitian symmetric manifolds

Hermitian symmetric manifolds are Hermitian manifolds which are homogeneous and such that every point has a symmetry preserving the Hermitian structure. The aim of these notes is to present an introduction to this important class of manifolds, trying to survey the several different perspectives from which Hermitian symmetric manifolds can be studied.Comment: 56 pages, expanded version. Written for the Proceedings of the CIME-CIRM summer course "Combinatorial Algebraic Geometry". Comments are still welcome

Treating some solid state problems with the Dirac equation

The ambiguity involved in the definition of effective-mass Hamiltonians for nonrelativistic models is resolved using the Dirac equation. The multistep approximation is extended for relativistic cases allowing the treatment of arbitrary potential and effective-mass profiles without ordering problems. On the other hand, if the Schrodinger equation is supposed to be used, our relativistic approach demonstrate that both results are coincidents if the BenDaniel and Duke prescription for the kinetic-energy operator is implemented. Applications for semiconductor heterostructures are discussed.Comment: 06 pages, 5 figure

Discovering New Physics in the Decays of Black Holes

If the scale of quantum gravity is near a TeV, the LHC will be producing one black hole (BH) about every second, thus qualifying as a BH factory. With the Hawking temperature of a few hundred GeV, these rapidly evaporating BHs may produce new, undiscovered particles with masses ~100 GeV. The probability of producing a heavy particle in the decay depends on its mass only weakly, in contrast with the exponentially suppressed direct production. Furthemore, BH decays with at least one prompt charged lepton or photon correspond to the final states with low background. Using the Higgs boson as an example, we show that it may be found at the LHC on the first day of its operation, even with incomplete detectors.Comment: 4 pages, 3 figure

Off-diagonal long-range order, cycle probabilities, and condensate fraction in the ideal Bose gas

We discuss the relationship between the cycle probabilities in the path-integral representation of the ideal Bose gas, off-diagonal long-range order, and Bose--Einstein condensation. Starting from the Landsberg recursion relation for the canonic partition function, we use elementary considerations to show that in a box of size L^3 the sum of the cycle probabilities of length k >> L^2 equals the off-diagonal long-range order parameter in the thermodynamic limit. For arbitrary systems of ideal bosons, the integer derivative of the cycle probabilities is related to the probability of condensing k bosons. We use this relation to derive the precise form of the \pi_k in the thermodynamic limit. We also determine the function \pi_k for arbitrary systems. Furthermore we use the cycle probabilities to compute the probability distribution of the maximum-length cycles both at T=0, where the ideal Bose gas reduces to the study of random permutations, and at finite temperature. We close with comments on the cycle probabilities in interacting Bose gases.Comment: 6 pages, extensive rewriting, new section on maximum-length cycle