Related papers: Sufficient conditions for non-zero entropy and fin…
We survey the connections between entropy, chaos, and independence in topological dynamics. We present extensions of two classical results placing the following notions in the context of symbolic dynamics: 1. Equivalence of positive entropy…
The first aims of this work are to endorse the advent of finitely additive set functions as equilibrium states and the possibility to replace the metric entropy by an upper semi-continuous map associated to a general variational principle.…
We study the entanglement entropy arising from coherent states and one--particle states. We show that it is possible to define a finite entanglement entropy by subtracting the vacuum entropy from that of the considered states, when the…
In this paper, an estimation of lower bound of topological entropy for coupled-expanding systems associated with transition matrices in compact Hausdorff spaces is given. Estimations of upper and lower bounds of topological entropy for…
Entropy notions for $\varepsilon$-incremental practical stability and incremental stability of deterministic nonlinear systems under disturbances are introduced. The entropy notions are constructed via a set of points in state space which…
This paper is concerned with strong Li-Yorke chaos induced by A-coupled-expansion for time-varying (i.e., nonautonomous) discrete systems in metric spaces. Some criteria of chaos in the strong sense of Li-Yorke are established via strict…
The entropic uncertainty relations are a very active field of scientific inquiry. Their applications include quantum cryptography and studies of quantum phenomena such as correlations and non-locality. In this work we find…
Currents of particles or energy in driven nonequilibrium steady states are known to satisfy certain symmetries, referred to as fluctuation relations, determining the ratio of the probabilities of positive fluctuations to negative ones. A…
We review generalized Fluctuation-Dissipation Relations which are valid under general conditions even in ``non-standard systems'', e.g. out of equilibrium and/or without a Hamiltonian structure. The response functions can be expressed in…
The notion of (non)contextuality pertains to sets of properties measured one subset (context) at a time. We extend this notion to include so-called inconsistently connected systems, in which the measurements of a given property in different…
Non-equilibrium and equilibrium thermodynamics of an interacting component in a special-relativistic multi-component system is discussed by use of an entropy identity. The special case of the corresponding free component is considered.…
We obtain some results of existence and continuity of physical measures through equilibrium states and apply these to non-uniformly expanding transformations on compact manifolds with non-flat critical sets, obtaining sufficient conditions…
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…
We consider distributions of ordered random vectors with given one-dimensional marginal distributions. We give an elementary necessary and sufficient condition for the existence of such a distribution with finite entropy. In this case, we…
Mixed monotone systems form an important class of nonlinear systems that have recently received attention in the abstraction-based control design area. Slightly different definitions exist in the literature, and it remains a challenge to…
Firstly, we calculate quantitatively decrease of entropy by the known formulas in the ordering phenomena and nucleation of thermodynamics of microstructure. They show again that a necessary condition of decrease of entropy in isolated…
We show that the naive application of the maximum entropy principle can yield answers which depend on the level of description, i.e. the result is not invariant under coarse-graining. We demonstrate that the correct approach, even for…
Entropy can signify different things: For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced and it can be difficult to ascertain their different importance and…
It is an open problem whether a homeomorphism on a compact metric space satisfying that each proper pair is either positively or negatively Li--Yorke, called completely Li--Yorke chaotic, can have positive entropy. In the present paper, an…
We derive a functional for the entropy contributed by any microscopic degrees of freedom as arising from their measurable pair correlations. Applicable both in and out of equilibrium, this functional yields the maximum entropy which a…