Related papers: Sequence entropy tuples and mean sensitive tuples
Motivated by the notion of intermediate dimensions introduced by Falconer et al., we introduce a continuum of topological entropies that are intermediate between the (Bowen) topological entropy and the lower and upper capacity topological…
In this note we construct measures of maximal entropy for a certain class of maps with critical points called Viana maps. The main ingredients of the proof are the non-uniform expansion features and the slow recurrence (to the critical set)…
We revisit the issue of defining the entropy of a spatial region in a broad class of quantum theories. In theories with explicit regularizations, working within an elementary but general algebraic framework applicable to matter and gauge…
We study how the Shannon entropy of sequences produced by an information source converges to the source's entropy rate. We synthesize several phenomenological approaches to applying information theoretic measures of randomness and memory to…
This paper studies when a sequence of probability measures on a metric space admit subsequential weak limits. A sufficient condition called sequential tightness is formulated, which relaxes some assumptions for asymptotic tightness used in…
This article deals with topological assumptions under which the minimal volume entropy of a closed manifold, and more generally of a finite simplicial complex, vanishes or is positive. In the first part of the article, we present…
Causal discovery is a fundamental problem in statistics and has wide applications in different fields. Transfer Entropy (TE) is a important notion defined for measuring causality, which is essentially conditional Mutual Information (MI).…
In this paper we study the set of Li-Yorke $d$-tuples and its $d$-dimensional Lebesgue measure for interval maps $T\colon [0,1] \to [0,1]$. If a topologically mixing $T$ preserves an absolutely continuous probability measure 9with respect…
Entanglement measures find frequent application in the study of topologically ordered systems, where the presence of topological order is reflected in an additional contribution to the entanglement of the system. Obtaining this topological…
The existence of the {\em typical set} is key for data compression strategies and for the emergence of robust statistical observables in macroscopic physical systems. Standard approaches derive its existence from a restricted set of…
For random dynamical systems, by summarizing the fundamental properties of Kifer's topological pressure we introduce the concept of random pressure functions, and define Ruelle's metric entropy for invariant measures. Employing the…
The ALEA Coq library formalizes measure theory based on a variant of the Giry monad on the category of sets. This enables the interpretation of a probabilistic programming language with primitives for sampling from discrete distributions.…
We investigate the concept of entropy in probabilistic theories more general than quantum mechanics, with particular reference to the notion of information causality recently proposed by Pawlowski et. al. (arXiv:0905.2992). We consider two…
Different notions of entropy play a fundamental role in the classical theory of dynamical systems. Unlike many other concepts used to analyze autonomous dynamics, both measure-theoretic and topological entropy can be extended quite…
Let $f : X\to X$ be a dominating meromorphic map on a compact K\"ahler manifold $X$ of dimension $k$. We extend the notion of topological entropy $h^l_{\mathrm{top}}(f)$ for the action of $f$ on (local) analytic sets of dimension $0\leq l…
We show how to determine the maximum and minimum possible values of one measure of entropy for a given value of another measure of entropy. These maximum and minimum values are obtained for two standard forms of probability distribution (or…
Entropies are fundamental measures of uncertainty with central importance in information theory and statistics and applications across all the quantitative sciences. Under a natural set of operational axioms, the most general form of…
It is well-known that $\epsilon$-stable sets have a deep connection with the topological entropy of dynamical systems. In the present paper, we investigate the relationships of three types of upper metric mean dimensions with potential…
We show that there is a compact topological space carrying a measure which is not a weak* limit of finitely supported measures but is in the sequential closure of the set of such measures. We construct compact spaces with measures of…
For a quantum-mechanical counting process we show ergodicity, under the condition that the underlying open quantum system approaches equilibrium in the time mean. This implies equality of time average and ensemble average for correlation…