Related papers: Comments on a Covariant Entropy Conjecture

Entropy is a quantity which is of great importance in physics and chemistry. The concept comes out of thermodynamics, proposed by Rudolf Clausius in his analysis of Carnot cycle and linked by Ludwig Boltzmann to the number of specific ways…

Entropy and energy are found to be closely tied on our quest for quantum gravity. We point out an interesting connection between the recently proposed outer entropy, a coarse-grained entropy defined for a compact spacetime domain motivated…

We propose a 'geometric Chevalley-Warning' conjecture, that is a motivic extension of the Chevalley-Warning theorem in number theory. It is equivalent to a particular case of a recent conjecture of F. Brown and O.Schnetz. In this paper, we…

The entanglement entropy has been historically studied by many authors in order to obtain quantum mechanical interpretations of the gravitational entropy. The discovery of AdS/CFT correspondence leads to the idea of holographic entanglement…

The emergence of trapped surfaces in solutions to the Einstein field equations is intimately tied to the well-posedness properties of the corresponding Cauchy problem in the low regularity regime. In this paper, we study the question of…

I argue that black hole entropy counts only those states of a black hole that can influence the outside, and attempt (with only partial success) to defend this claim against various objections, all but one coming from string theory.…

To compute the spectrum of bubble collisions seen by an observer in an eternally-inflating multiverse, one must choose a measure over the diverging spacetime volume, including choosing an "initial" hypersurface below which there are no…

The approximability of a convex body is a number which measures the difficulty to approximate that body by polytopes. We prove that twice the approximability is equal to the volume entropy for a Hilbert geometry in dimension two end three…

Trapped surfaces are studied as inner boundary for the Einstein vacuum constraint equations. The trapped surface condition can be written as a non linear boundary condition for these equations. Under appropriate assumptions, we prove…

This paper deals with the existence of global weak solutions for a wide class of (multiple species) cross-diffusions systems. The existence is based on two different ingredients: an entropy estimate giving some gradient control and a…

We introduce a new variant of the coarse Baum-Connes conjecture designed to tackle coarsely disconnected metric spaces called the boundary coarse Baum-Connes conjecture. We prove this conjecture for many coarsely disconnected spaces that…

We consider the situation when a globally defined four-dimensional field system is separated on two entangled sub-systems by a dynamical (random) two-dimensional surface. The reduced density matrix averaged over ensemble of random surfaces…

We use the holographic proposal for calculating entanglement entropies to determine the boundary entropy of defects in strongly coupled two-dimensional conformal field theories. We study several examples including the Janus solution and…

In this letter we propose the use of physics techniques for entropy determination on constrained parameter optimization problems. The main feature of such techniques, the construction of an unbiased walk on energy space, suggests their use…

We present a positive solution to the so-called Bernoulli Conjecture concerning the characterization of sample boundedness of Bernoulli processes. We also discuss some applications and related open problems.

The holographic bound that the entropy (log of number of quantum states) of a system is bounded from above by a quarter of the area of a circumscribing surface measured in Planck areas is widely regarded a desideratum of any fundamental…

Entropy arises in strong interactions by a dynamical separation of ``partons'' from unobservable ``environment'' modes due to confinement. For interacting scalar fields we calculate the statistical entropy of the observable subsystem.…

We define the stretched future light cone, a timelike hypersurface composed of the worldlines of radially accelerating observers with constant and uniform proper acceleration. By attributing temperature and entropy to this hypersurface, we…

Entanglement entropy for spatial subregions is difficult to define in string theory because of the extended nature of strings. Here we propose a definition for Bosonic open strings using the framework of string field theory. The key…

The purpose of this paper is to generalize the variational principle, which states that the topological entropy is equal to the supremum of the measure theoretical entropies and also the minimum of the metric theoretical entropies, to…