Related papers: On singular limits of relative entropies
We introduce the telescopic relative entropy (TRE), which is a new regularisation of the relative entropy related to smoothing, to overcome the problem that the relative entropy between pure states is either zero or infinity and therefore…
We consider logarithmic conformal field theories near a boundary and derive the general form of one and two point functions. We obtain results for arbitrary and two dimensions. Application to two dimensional magnetohydrodynamics is…
For a general class of lattice-spin systems, we prove that an abstract Gaussian concentration bound implies positivity of lower relative entropy density. As a consequence we obtain uniqueness of translation-invariant Gibbs measures from the…
{In 1+1 dimensional conformal field theory with a boundary the boundary contribution to the entanglement entropy is determined by a single number $g$ effectively counting the boundary degrees of freedom. In contrast, in 1+1 dimensional…
It is pointed out that the entanglement entropy of quantum fields near the horizon of a two-dimensional black hole can be derived by means of the conformal field theory. This can be done in a way analogous to the computation of the entropy…
The present paper studies continuity of generalized entropy functions and relative entropies defined using the notion of a deformed logarithmic function. In particular, two distinct definitions of relative entropy are discussed. As an…
We introduce a new generalization of relative entropy to non-negative vectors with sums $\gt 1$. We show in a purely combinatorial setting, with no probabilistic considerations, that in the presence of linear constraints defining a convex…
We extend the relative entropy identity to the class of hyperbolic-parabolic systems whose hyperbolic part is symmetrizable. The resulting identity, in the general theory, is useful to provide stability of viscous solutions and yields a…
We provide non-asymptotic, relative deviation bounds for the eigenvalues of empirical covariance and Gram matrices in general settings. Unlike typical uniform bounds, which may fail to capture the behavior of smaller eigenvalues, our…
For discrete-time stochastic processes, there is a close connection between return/waiting times and entropy. Such a connection cannot be straightforwardly extended to the continuous-time setting. Contrarily to the discrete-time case one…
In this paper we consider entanglement entropies in two-dimensional conformal field theories in the presence of topological interfaces. Tracing over one side of the interface, the leading term of the entropy remains unchanged. The interface…
In the vacuum state of a CFT, the entanglement entropy of singular surfaces contains a logarithmic universal term which is only due to the singularity of the entangling surface. We consider the relevant perturbation of a three dimensional…
We review old and recent finite de Finetti theorems in total variation distance and in relative entropy, and we highlight their connections with bounds on the difference between sampling with and without replacement. We also establish two…
We provide an informal overview of recent developments concerning the singular local limit of nonlocal conservation laws. In particular, we discuss some counterexamples to convergence and we highlight the role of numerical viscosity in the…
We define the notions of relative $e$-spectra, with respect to $E$-operators, relative closures, and relative generating sets. We study properties connected with relative $e$-spectra and relative generating sets.
We consider the symmetry resolution of relative entropies in the 1+1 dimensional free massless compact boson conformal field theory (CFT) which presents an internal $U(1)$ symmetry. We calculate various symmetry resolved R\'enyi relative…
A criterion and necessary conditions for convergence (local continuity) of the quantum relative entropy are obtained. Some applications of these results are considered. In particular, the preservation of local continuity of the quantum…
This paper is a survey about recent developments in the local entropy theory for topological dynamical systems and continuous group actions, with particular emphasis on the connections with other areas of dynamical systems and mathematics.
We study the question of how reliably one can distinguish two quantum field theories (QFTs). Each QFT defines a probability distribution on the space of fields. The relative entropy provides a notion of proximity between these distributions…
We study the entanglement entropy of theories that are derived from relevant perturbation of given CFTs for regions with a singular boundary by using the AdS/CFT correspondence. In the smooth case, it is well known that a relevant…