Related papers: Entropy Bound and a Geometrically Nonsingular Univ…
For a manifold-with-boundary moving by mean curvature flow, the entropy at a later time is bounded by the entropy at an earlier time plus a boundary term. This paper controls the boundary term in a geometrically natural way. In particular,…
A dynamical estimate is given for the Boltzmann entropy of the Universe, under the simplifying assumptions provided by Newtonian cosmology. We first model the cosmological fluid as the probability fluid of a quantum-mechanical system. Next,…
We are concerned with spherically symmetric solutions to the Euler equations for the multi-dimensional compressible fluids, which have many applications in diverse real physical situations. The system can be reduced to one dimensional…
We consider the Cauchy problem for the isentropic compressible Euler equations in a three-dimensional periodic domain under general pressure laws. For any smooth initial density away from the vacuum, we construct infinitely many entropy…
According to the Ryu-Takayanagi prescription, the entanglement entropy of subsystems in the boundary conformal field theory (CFT) is proportional to the area of extremal surfaces in bulk asymptotically Anti-de Sitter (AdS) spacetimes. The…
Two spatial regions $B$ and $R$ are hyperentangled if the generalized entropy satisfies $S_{\text{gen}}^{B\cup R}<S_{\text{gen}}^R$. If in addition all future (or all past) directed inward null shape deformations of $B$ decrease…
We argue that every finite piecewise smooth spacelike two-surface of spacetime possesses an entropy which is, in natural units, one quarter of its area. However, the thermodynamical properties of a two-surface become apparent only to the…
We are concerned with the global existence of entropy solutions for the compressible Euler equations describing the gas flow in a nozzle with general cross-sectional area, for both isentropic and isothermal fluids. New viscosities are…
In this paper, we introduce two bounds which we call the Upper Differential Entropy and the Lower Differential Entropy for an infinite family of intervals(strips) in quantum field theory. The two bounds are equal provided that the theory is…
In any static spacetime the quasilocal Tolman mass contained within a volume can be reduced to a Gauss-like surface integral involving the flux of a suitably defined generalized surface gravity. By introducing some basic thermodynamics, and…
We extend Bousso's notion of a lightsheet - a surface where entropy can be defined in a way so that the entropy bound is satisfied - to more general surfaces. Intuitively these surfaces may be regarded as deformations of the Bousso choice;…
We consider the volume entropy of closed flat surfaces of genus $g\geq 2$ and area 1. We show that a sequence of flat surfaces diverges in the moduli space if and only if the volume entropy converges to infinity. Equivalently the Hausdorff…
Motivated by the notion that the mathematics of gravity can be reproduced from a statistical requirement of maximal entropy, we study the consequence of introducing an entropic source term in the Einstein-Hilbert action. For a spatially…
We conjecture a universal upper bound to the entropy of a rotating system. The entropy bound follows from application of the generalized second law of thermodynamics to an idealized gedanken experiment in which an entropy-bearing rotating…
The universe time-asymmetry is essentially produced by its low-entropy unstable initial state. Using quanlitative arguments, Paul Davies has demonstrated that the universe expansion may diminish the entropy gap, therefore explaining its…
We investigate the behavior of the entanglement entropy of a confining gauge theory near cosmological singularities using gauge/gravity duality. As expected, the coefficients of the UV divergent terms are given by simple geometric…
We consider critical models in one dimension. We study the ground state in thermodynamic limit [infinite lattice]. Following Bennett, Bernstein, Popescu, and Schumacher, we use the entropy of a sub-system as a measure of entanglement. We…
The conditions for validity of the Causal Entropy Bound (CEB) are verified in the context of non-singular cosmologies with classical sources. It is shown that they are the same conditions that were previously found to guarantee validity of…
Experimental and theoretical results about entropy limits for macroscopic and single-particle systems are reviewed. It is clarified when it is possible to speak about a quantum of entropy, given by the Boltzmann constant k, and about a…
In this paper we seek to understand what current knowledge of entanglement entropies suggests about the appropriate way to interpret the covariant entropy bound. We first begin by arguing that just as in the classical case, a universal…