Related papers: Telescopic Relative Entropy--II Triangle inequalit…

The geometric entropy in quantum field theory is not a Lorentz scalar and has no invariant meaning, while the black hole entropy is invariant. Renormalization of entropy and energy for reduced density matrices may lead to the negative free…

Information entropy and its extension, which are important generalization of entropy, have been applied in many research domains today. In this paper, a novel generalized relative entropy is constructed to avoid some defects of traditional…

In [Gallego and Aolita, Physical Review X 5, 041008 (2015)], the authors proposed a definition for the relative entropy of steering and showed that the resulting quantity is a convex steering monotone. Here we advocate for a different…

The R\'enyi and Shannon entropies are information-theoretic measures which have enabled to formulate the position-momentum uncertainty principle in a much more adequate and stringent way than the (variance-based) Heisenberg-like relation.…

In symmetric teleparallel geometry the curvature and torsion tensors are assumed to vanish identically, while the dynamics of gravity is encoded by nonmetricity. Here the spatially homogeneous and isotropic connections that can accompany…

We derive a measurement-independent asymptotic continuity bound on the observational entropy for general POVM measurements, making essential use of its property of bounded concavity. The same insight is used to obtain continuity bounds for…

We establish a connection between barcode entropy and metric entropy. Namely, we show that the barcode entropy bounds the metric entropy from below for a measure from a specific class of invariant measures associated with a pair of…

Topological feedback entropy (TFE) was introduced in 2004 to measure the intrinsic rate at which a continuous, fully observed, deterministic control system generates information for controlled set-invariance. In this paper, we generalise…

Entanglement entropy in topologically ordered matter phases has been computed extensively using various methods. In this paper, we study the entanglement entropy of topological phases in two-spaces from a new perspective---the perspective…

The holographic representation of the entanglement entropy of four dimensional conformal field theories is studied. By generalizing the replica trick the anomalous terms in the entanglement entropy are evaluated. The same terms in the…

In the invariant approach to special relativity (SR), which we call the ''true transformations (TT) relativity,'' a physical quantity in the four-dimensional spacetime is mathematically represented either by a true tensor or equivalently by…

Motivated by the notion that the mathematics of gravity can be reproduced from a statistical requirement of maximal entropy, we study the consequence of introducing an entropic source term in the Einstein-Hilbert action. For a spatially…

We discuss the entropy generation in quantum tunneling of a relativistic particle under the influence of a time varying force with the help of squeezing formalism. It is shown that if one associates classical coarse grained entropy to the…

The reversibility and recurrence paradoxes are key issues that have been left unsolved in researches on the foundation of thermodynamics since the 19th century. This article shows that (1) the reversibility paradox can be overcome if we pay…

Following a growing number of studies that, over the past 15 years, have established entropy inequalities via ideas and tools from additive combinatorics, in this work we obtain a number of new bounds for the differential entropy of sums,…

Topological entropy or spatial entropy is a way to measure the complexity of shift spaces. This study investigates the relationships between the spatial entropy and the various periodic entropies which are computed by skew-coordinated…

Tsallis relative operator entropy was defined as a parametric extension of relative operator entropy and the generalized Shannon inequalities were shown in the previous paper. After the review of some fundamental properties of Tsallis…

We show that Frenkel's integral representation of the quantum relative entropy provides a natural framework to derive continuity bounds for quantum information measures. Our main general result is a dimension-independent semi-continuity…

Equations that follow from the Navier-Stokes equation and incompressibility but with no other approximations are "exact.". Exact equations relating second- and third-order structure functions are studied, as is an exact incompressibility…

In this paper, we derive exponential ergodicity in relative entropy for general kinetic SDEs under a partially dissipative condition. It covers non-equilibrium situations where the forces are not of gradient type and the invariant measure…