Related papers: The Bekenstein Bound
The various entropy bounds that exist in the literature suggest that spacetime is fundamentally discrete, and hint at an underlying relationship between geometry and "information". The foundation of this relationship is yet to be uncovered,…
Let $S(\rho)=- Tr (\rho \log\rho)$ be the von Neumann entropy of an $N$-dimensional quantum state $\rho$ and $e_2(\rho)$ the second elementary symmetric polynomial of the eigenvalues of $\rho$. We prove the inequality $S(\rho) \le c(N)…
We examine Bousso's covariant entropy bound conjecture in the context of radiation filled, spatially flat, Friedmann-Robertson-Walker models. The bound is violated near the big bang. However, the hope has been that quantum gravity effects…
We propose a universal inequality that unifies the Bousso bound with the classical focussing theorem. Given a surface $\sigma$ that need not lie on a horizon, we define a finite generalized entropy $S_\text{gen}$ as the area of $\sigma$ in…
In this paper, we identify the change in the boundary full modular hamiltonian with the bulk observables for spherically symmetric excitations. The identification is demonstrated for perturbative as well as non perturbative excitations. We…
We give response to the question: in infinite dimension states,given a state with energy bounded by E, we can write the state as a countable convex combination of pure states with energy bounded by E. We review the Alicki-Fannes-Winter…
We point out that aspects of quantum mechanics can be derived from the holographic principle, using only a perturbative limit of classical general relativity. In flat space, the covariant entropy bound reduces to the Bekenstein bound. The…
Exact calculations are given for the Casimir energy for various fields in $R\times S^3$ geometry. The Green's function method naturally gives a result in a form convenient in the high-temperature limit, while the statistical mechanical…
Boltzmann's principle S(E,N,V)=k\ln W relates the entropy to the geometric area e^{S(E,N,V)} of the manifold of constant energy in the N-body phase space. From the principle all thermodynamics and especially all phenomena of phase…
An approach to quantum gravity and cosmology is proposed based on a synthesis of four elements: 1) the Bekenstein bound and the related holographic hypothesis of 't Hooft and Susskind, 2) topological quantum field theory, 3) a new approach…
If the N bosons that compose an ideal Bose-Einstein gas with energy E and volume V are each assumed to have the average energy of the system E/N, the entropy is easily expressed in terms of the number of bosons N and the number of…
We take the view that the standard von Neumann definition, in which the entropy $S^{vN}$ of a pure state is zero, is in evident conflict with the statement of the second law that the entropy of the universe $S_{univ}$ increases in…
We show that the nonequilibrium entropy production for a driven quantum system is larger than the Bures length, the geometric distance between its actual state and the corresponding equilibrium state. This universal lower bound generalizes…
We prove an area law for the entanglement entropy in gapped one dimensional quantum systems. The bound on the entropy grows surprisingly rapidly with the correlation length; we discuss this in terms of properties of quantum expanders and…
This paper consists of three steps. In the first, we prove that the Bekenstein-Hawking entropy is the unique expression of black hole entropy. Our proof is constructed in the framework of thermodynamics without any statistical discussion.…
In this letter it is proposed to study the Bekenstein's $\xi(4)$ calculation of the $S/E$ bound for more general geometries. It is argued that, using some relations among eigenvalues obtained in the context of Spectral Geometry, it is…
By regarding the Hawking-Bekenstein entropy of Schwarzschild black hole horizons as a non-extensive Tsallis entropy, its formal logarithm, the R\'enyi entropy, is considered. The resulting temperature - horizon-radius relation has the same…
A computer, in order to perform a given computation, requires a certain amount of space (memory) and a certain amount of time (runtime). This leaves certain computations beyond reach due to technological limits on processing speed and…
Bekenstein's generalized second law (GSL) of thermodynamics asserts that the sum of black-hole entropy, $S_{\text{BH}}=Ac^3/4\hbar G$ (here $A$ is the black-hole surface area), and the ordinary entropy of matter and radiation fields in the…
It has been proposed that the entropy of any object must satisfy fundamental (holographic or Bekenstein) bounds set by the object's size and perhaps its energy. However, most discussions of these bounds have ignored the possibility that…