Related papers: Relative entropy for compact Riemann surfaces
We study a notion of relative entropy for certain hypersurfaces in hyperbolic space. We relate this quantity to the renormalized area introduced by Graham-Witten[RW99]. We also obtain a monotonicity formula for relative entropy applied to…
We consider a massive scalar field with arbitrary coupling in $\mathbf{S}^{1}\times \mathbf{S}^{3}$ space, which mimics the thermal expanding universe, and calculate explicitly all relevant thermodynamical functions in the low- and…
We define a Bowen-Series like map for every geometric presentation of a co-compact surface group and we prove that the volume entropy of the presentation is the topological entropy of this particular (circle) map. Finally we find the…
Relative entropy is a fundamental class of distances between probability distributions, with widespread applications in probability theory, statistics, and machine learning. In this work, we study relative entropy from a categorical…
The entropy of a hypersurface is a geometric invariant that measures complexity and is invariant under rigid motions and dilations. It is given by the supremum over all Gaussian integrals with varying centers and scales. It is monotone…
We obtain the analytic solution of the Friedmann equation for fully realistic cosmologies including radiation, non-relativistic matter, a cosmological constant $\lambda$ and arbitrary spatial curvature $\kappa$. The general solution for the…
We analyze the renormalization group (RG) flow of the temperature independent term of the entropy in the high temperature limit \beta/a<<1 of a massive field theory in 3-dimensional spherical spaces M_3 with constant curvature 6/a^2. For…
Macroscopic fields like electromagnetic, MHD, acoustic or gravitational waves are usually described by classical wave equations with possible additional damping terms and coherent sources. The aim of this paper is to develop a complete…
The ground state density matrix for a massless free field is traced over the degrees of freedom residing inside an imaginary sphere; the resulting entropy is shown to be proportional to the area (and not the volume) of the sphere. Possible…
Relative entropy is a powerful measure of the dissimilarity between two statistical field theories in the continuum. In this work, we study the relative entropy between Gaussian scalar field theories in a finite volume with different masses…
The coefficient of the logarithmic term in the entropy on even spheres is re-computed by the local technique of integrating the finite temperature energy density up to the horizon on static d--dimensional de Sitter space and thence finding…
A kinetic theory of relativistic gases in a two-dimensional space is developed in order to obtain the equilibrium distribution function and the expressions for the fields of energy per particle, pressure, entropy per particle and heat…
Expanding the black hole thermodynamics from the horizon to achronal Cauchy hypersurface, the general relation between the Einstein equation and thermodynamics is established. Starting from trivial entropy that is generalized by…
We consider a static self-gravitating perfect fluid system in Lovelock gravity theory. For a spacial region on the hypersurface orthogonal to static Killing vector, by the Tolman's law of temperature, the assumption of a fixed total…
Entropy is a natural geometric quantity measuring the complexity of a surface embedded in $\mathbb{R}^3$. For dynamical reasons relating to mean curvature flow, Colding-Ilmanen-Minicozzi-White conjectured that the entropy of any closed…
Given a closed, orientable surface of constant negative curvature and genus $g \ge 2$, we study the topological entropy and measure-theoretic entropy (with respect to a smooth invariant measure) of generalized Bowen--Series boundary maps.…
We establish the irreversibility of renormalization group flows on a pointlike defect inserted in a $d$-dimensional Lorentzian conformal field theory. We identify the impurity entropy $g$ with the quantum relative entropy in two equivalent…
We consider quantum algebras of observables associated with subregions in theories of Einstein gravity coupled to matter in the $G_N\rightarrow 0$ limit. When the subregion is spatially compact or encompasses an asymptotic boundary, we…
For a locally compact sofic group continuously acting on a compact metric space, we first study the relative sofic entropy and prove an additive inequality relating sofic entropy and relative sofic entropy. Moreover, it is shown that the…
The notion of entropy appears in many fields and this paper is a survey about entropies in several branches of Mathematics. We are mainly concerned with the topological and the algebraic entropy in the context of continuous endomorphisms of…