Related papers: Boundary entropy spectra as finite subsums

Close connections between various notions of entropy and the apparatus of category theory have been observed already in the 1980s and more vigorously developed in the past ten years. The starting point of the paper is the recent categorical…

We derive general bounds on the probability that the empirical first-passage time $\overline{\tau}_n\equiv \sum_{i=1}^n\tau_i/n$ of a reversible ergodic Markov process inferred from a sample of $n$ independent realizations deviates from the…

We establish upper bounds on the size of the largest subset of $\{1,2,\dots,N\}$ lacking nonzero differences of the form $h(p_1,\dots,p_{\ell})$, where $h\in \mathbb{Z}[x_1,\dots,x_{\ell}]$ is a fixed polynomial satisfying appropriate…

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…

Let $\sum_{n=1}^\infty x_n$ be a conditionally convergent series in a Banach space and let $\tau$ be a permutation of natural numbers. We study the set $\operatorname{LIM}(\sum_{n=1}^\infty x_{\tau(n)})$ of all limit points of a sequence…

We study the entanglement entropies of an interval adjacent to the boundary of the half line for the free fermionic spinless Schr\"odinger field theory at finite density and zero temperature, with either Neumann or Dirichlet boundary…

We establish several Schur-convexity type results under fixed variance for weighted sums of independent gamma random variables and obtain nonasymptotic bounds on their R\'enyi entropies. In particular, this pertains to the recent results by…

We revisit entropic formulations of the uncertainty principle for an arbitrary pair of positive operator-valued measures (POVM) $A$ and $B$, acting on finite dimensional Hilbert space. Salicr\'u generalized $(h,\phi)$-entropies, including…

Entanglement entropy appears as a central property of quantum systems in broad areas of physics. However, its precise value is often sensitive to unknown microphysics, rendering it incalculable. By considering parametric dependence on…

This article investigates the possibility to use the class entropy of the output of a connectionist phoneme recogniser to predict time boundaries between phonetic classes. The rationale is that the value of the entropy should increase in…

We present a number of explicit calculations of Renyi and entanglement entropies in situations where the entangling surface intersects the boundary in $d$-dimensional Minkowski spacetime. When the boundary is a single plane we compute the…

Entropy rate is a real valued functional on the space of discrete random sources which lacks a closed formula even for subclasses of sources which have intuitive parameterizations. A good way to overcome this problem is to examine its…

We introduce a natural definition for sums of the form \[ \sum_{\nu=1}^x f(\nu) \] when the number of terms x is a rather arbitrary real or even complex number. The resulting theory includes the known interpolation of the factorial by the…

We prove a sharp bound between sampling numbers and entropy numbers in the uniform norm for bounded convex sets of bounded functions.

The aim of the present dissertation is to analyze the meaning of the entropy bounds of the holographic sector once tested for statistical ensembles of particles, in order to deeper investigate the nature of these constraints and their…

Using periodic points we study a notion of entropy with values in the p-adic numbers. This is done for actions of countable discrete residually finite groups $\Gamma$. For suitable $\Gamma = \mathbb{Z}^d$-actions we obtain p-adic analogues…

We investigate the R\'enyi entropy of independent sums of integer valued random variables through Fourier theoretic means, and give sharp comparisons between the variance and the R\'enyi entropy, for Poisson-Bernoulli variables. As…

We consider a transitive action of a finitely generated group $G$ and the Schreier graph $\Gamma$ defined by this action for some fixed generating set. For a probability measure $\mu$ on $G$ with a finite first moment we show that if the…

A common approach for the numerical simulation of wave propagation on a spatially unbounded domain is to truncate the domain via an artificial boundary, thus forming a finite computational domain with an outer boundary. Absorbing boundary…

The geometric entanglement entropy of a quantum field in the vacuum state is known to be divergent and, when regularized, to scale as the area of the boundary of the region. Here we introduce an operational definition of the entropy of the…