Narrow Results

There has been, quite recently, a discussion on how holographic-inspired bounds might be used to encompass the present-day dark energy and early-universe inflation into a single paradigm. In the current treatment, we point out an inconsistency in the proposed framework and then provide a viable resolution. We also elaborate on some of the implications of this framework and further motivate the proposed holographic connection. The manuscript ends with a more speculative note on cosmic time as an emergent (holographically induced) construct.

Just as gravitons can carry energy, they can also be used to transmit information. It follows that an entropy should be associated with gravitational degrees of freedom, independent of the presence or absence of black holes. In this essay, we discuss how one might count gravitational entropy given a classical gravitational field. Our suggestion is motivated by a derivation of the covariant entropy bound in which a gravitational term appears naturally.

The Bousso entropy bound is investigated for static, spherically symmetric configurations of an ideal gas with a Bose–Einstein or Fermi–Dirac distribution function. Gas of massive particles is considered. This paper is continuation of the previous work concerning the massless case. Special attention is devoted to light sheets generated by spheres. Conditions under which the Bousso bound can be violated are discussed and it is shown that a possible violating region cannot be arbitrarily large and that it is contained inside a sphere of unit Planck radius if the number of independent spin states g_s is small enough. It is also shown that the central temperature must exceed the Planck temperature in order to get a violation of the Bousso bound for g_s which is not too large. The situation for higher-dimensional space–times is also discussed and the conditions of Flanagan, Marolf and Wald are investigated.

A recently formulated universal lower bound to the characteristic relaxation times of perturbed thermodynamic systems, derived from quantum information theory and (classical) thermodynamics and known to be saturated for (certain) black holes, is investigated in the light of the gravity–thermodynamics connection. A statistical-mechanical property, unrelated to gravity, essential for the validity of the generalized covariant entropy bound, namely the existence of a lower-limiting value l* for the size of thermodynamic systems, is found to provide a way to understand this universal relaxation bound, thus regardless of the kind of foundations (i.e. whether conventional or information-based) of the statistical-mechanical description. As a by-product an example of a conventional system (i.e. not a black hole) seemingly saturating the universal relaxation bound is provided.

Entropy of all systems that we understand well is proportional to their volumes except for black holes given by their horizon area. This makes the microstates of any quantum theory of gravity drastically different from the ordinary matter. Because of the assumption that black holes are the maximum entropy states, there have been many conjectures that put the area, defined one way or another, as a bound on the entropy in a given region of spacetime. Here, we construct a simple model with entropy proportional to volume which exceeds the entropy of a single black hole. We show that a homogeneous cosmology filled with this gas exceeds one of the tightest entropy bounds, the covariant entropy bound and discuss the implications.

The aim of this paper is to analyze the meaning of the entropy bounds of the holographic sector once tested for statistical ensembles of particles, in order to deeply investigate the nature of these constraints and their mutual links. From the universal entropy bound (UEB) simple time constraints can be argued, which are manifestations of the discrete nature of the spacetime and of the presence of ultimate spacetime scales. From the combined effort of the UEB and of the Holographic bound by 't Hooft and Susskind, an entropy density bound as a function of temperature is achieved.

In this essay, we argue that certain aspects of the measurement require revision in Quantum Gravity. Using entropic arguments, we propose that the number of measurement outcomes and the accuracy (or the range) of the measurement are limited by the entropy of the black hole associated with the observer’s scale. This also implies the necessity of modifying the algebra of commutation relationships to ensure a finite representation of observables, changing the Heisenberg Uncertainty Principle in this manner.

We introduce a new framework for studying two-dimensional conservation laws by compensated compactness arguments. Our main result deals with 2D conservation laws which are nonlinear in the sense that their velocity fields are a.e. not co-linear. We prove that if u^ε is a family of uniformly bounded approximate solutions of such equations with H^-1-compact entropy production and with (a minimal amount of) uniform time regularity, then (a subsequence of) u^ε convergences strongly to a weak solution. We note that no translation invariance in space — and in particular, no spatial regularity of u(·, t) is required. Our new approach avoids the use of a large family of entropies; by a judicious choice of entropies, we show that only two entropy production bounds will suffice. We demonstrate these convergence results in the context of vanishing viscosity, kinetic BGK and finite volume approximations. Finally, the intimate connection between our 2D compensated compactness arguments and the notion of multi-dimensional nonlinearity based on kinetic formulation is clarified.