Related papers: Bound states and the Bekenstein bound
According to the entropy bound, the entropy of a complete physical system can be universally bounded in terms of its circumscribing radius and total gravitating energy. Page's three recent candidates for counterexamples to the bound are…
While von Neumann entropies for subregions in quantum field theory universally contain ultraviolet divergences, differences between von Neumann entropies are finite and well-defined in many physically relevant scenarios. We demonstrate that…
Finite physical systems have only a finite amount of distinct state. This finiteness is fundamental in statistical mechanics, where the maximum number of distinct states compatible with macroscopic constraints defines entropy. Here we show…
A generalized particle system interacting with a massless Bose field is investigated. We assume regularity conditions for the commutation relations of the interaction and annihilation operators. It is proven that if the ground state exists,…
We study entropy--coherence relations near rank-deficient support boundaries in finite-dimensional quantum systems. For block-diagonal reference states, we establish support-sensitive coercivity estimates showing that the entropy cost of…
We show that for any invariant measure $\mu$ on a free group shift system, there are two numbers $h^\flat \leq h^\sharp$ which in some sense are the typical upper and lower sofic entropy values. We also give a condition under which $h^\flat…
In quantum field theories defined on a spacetime with boundaries, the entanglement entropy exhibits subleading, boundary-induced corrections to the ubiquitous area law. At critical points described by conformal field theories (CFTs), and…
We investigate entanglement measures in the infinite-dimensional regime. First, we discuss the peculiarities that may occur if the Hilbert space of a bi-partite system is infinite-dimensional, most notably the fact that the set of states…
We study the free XXZ quantum spin model defined on a ring of size $L$ and show that the bipartite entanglement entropy of eigenstates belonging to the first energy band above the vacuum ground state satisfies a logarithmically corrected…
An explicit calculation is given of the entropy/energy ratio for the TM modes of the electromagnetic field in the half Einstein universe. This geometry provides a mathematically convenient and physically instructive example of how the…
We discuss whether black hole entropy counts short or long range microstates in quantum gravity. In brick wall and induced gravity models the entropy arises due to short distance correlations across the event horizon cut off at the Planck…
We examine distinct measures of fermionic entanglement in the exact ground state of a finite superconducting system. It is first shown that global measures such as the one-body entanglement entropy, which represents the minimum relative…
Calculations of the entanglement entropy of a spatial region in continuum quantum field theory require boundary conditions on the fields at the fictitious boundary of the region. These boundary conditions impact the treatment of the zero…
Entropy bounds in black hole physics, based on a wide variety of different approaches, have had a long and distinguished history. Recently the current authors have turned attention to uncollapsed systems and obtained a robust entropy bound…
Entanglement in a pure state of a many-body system can be characterized by the R\'enyi entropies $S^{(\alpha)}=\ln\textrm{tr}(\rho^\alpha)/(1-\alpha)$ of the reduced density matrix $\rho$ of a subsystem. These entropies are, however,…
We consider general stochastic systems of interacting particles with noise which are relevant as models for the collective behavior of animals, and rigorously prove that in the mean-field limit the system is close to the solution of a…
We analyze the problem of quantifying entanglement in pure and mixed states of fermionic systems with fixed number parity yet not necessarily fixed particle number. The "mode entanglement" between one single-particle level and its…
We establish that unitarity of scattering amplitudes imposes universal entropy bounds. The maximal entropy of a self-sustained quantum field object of radius R is equal to its surface area and at the same time to the inverse running…
Let $H_k$, $k\in {\mathbb{N}}$, be the Hilbert spaces of geometric quantization on a K\"ahler manifold $M$. With two points in $M$ we associate a Bell-type state $b_k \in H_k\otimes H_k$. When $M$ is compact or when $M$ is ${\mathbb{C}}^n$,…
We consider the Euler system of compressible and entropic gaz dynamics in a bounded open domain with wall boundary condition. We prove the existence and the stability of families of solutions which correspond to a ground state plus a large…