Related papers: Additivity properties of sofic entropy and measure…

Shearer's inequality bounds the sum of joint entropies of random variables in terms of the total joint entropy. We give another lower bound for the same sum in terms of the individual entropies when the variables are functions of…

We introduce the notion of induced topological pressure for countable state Markov shifts with respect to a non-negative scaling function and an arbitrary subset of finite words. Firstly, the scaling function allows a direct access to…

Observing how long a dynamical system takes to return to some state is one of the most simple ways to model and quantify its dynamics from data series. This work proposes two formulas to estimate the KS entropy and a lower bound of it, a…

Motivated, in part, by the desire to develop an information-theoretic foundation for compound Poisson approximation limit theorems (analogous to the corresponding developments for the central limit theorem and for simple Poisson…

Measuring the average information that is necessary to describe the behaviour of a dynamical system leads to a generalization of the Kolmogorov-Sinai entropy. This is particularly interesting when the system has null entropy and the…

In this paper, we introduce the notions of lowerable, D-lowerable, P-lowerable, hereditarily lowerable, and hereditarily uniformly lowerable for countably infinite amenable group actions. We show that a system with finite entropy is…

We examine several definitions of soficity for monoids obtained by generalizing various definitions of sofic groups. They are not all equivalent and include the definition recently introduced by Ceccherini-Silberstein and Coornaert. One of…

We introduce a composition of quantum states of a bipartite system which is based on the reshuffling of density matrices. This non-Abelian product is associative and stems from the composition of quantum maps acting on a simple quantum…

Recently, Suyari has proposed a generalization of Shannon-Khinchin axioms, which determines a class of entropies containing the well-known Tsalis and Havrda-Charvat entropies [H. Suyari, IEEE Trans. Inf. Theory, vol. 50, pp. 1783-1787, Aug.…

Misiurewicz[19]introducedtheconceptofpseudo-entropyandproved this quantity coincides with topological entropy. Richeson et al. [21] obtained the lower bounded of topological entropy by means of the definition of pseudo-entropy. This paper…

The dynamics of symbolic systems, such as multidimensional subshifts of finite type or cellular automata, are known to be closely related to computability theory. In particular, the appropriate tools to describe and classify topological…

We construct a family of shift spaces with almost specification and multiple measures of maximal entropy. This answers a question from Climenhaga and Thompson [Israel J. Math. 192 (2012), no. 2, 785--817]. Elaborating on our examples we…

Entropy of categorical dynamics is defined by Dmitrov-Haiden-Katzarkov-Kontsevich. Motivated by the fundamental theorem of the topological entropy due to Gromov-Yomdin, it is natural to ask an equality between the entropy and the spectral…

We propose a unifying picture where the notion of generalized entropy is related to information theory by means of a group-theoretical approach. The group structure comes from the requirement that an entropy be well defined with respect to…

We calculate slow entropy type invariant introduced by A. Katok and J.-P. Thouvenot in [5] for higher rank smooth abelian actions for two leading cases: when the invariant measure is absolutely continuous and when it is hyperbolic. We…

Let $M$ be a compact surface with boundary. We are interested in the question of how a group action on $M$ permutes a finite invariant set $X \subset int(M)$. More precisely, how the algebraic properties of the induced group of permutations…

We develop an information-theoretic formulation of stochastic dynamics in which the fundamental stochastic variable is the total action connecting spacetime points, rather than individual paths. By maximizing Shannon entropy over a joint…

We introduce a notion of entropy for automorphisms of discrete groups which admit amenable actions on a compact space. This entropy is dual to classical topological entropy in the sense that if G is discrete and abelian then our notion of…

The topological entropy of piecewise affine maps is studied. It is shown that singularities may contribute to the entropy only if there is angular expansion and we bound the entropy via the expansion rates of the map. As a corollary we…

In the paper we throw the first light on studying systematically the local entropy theory for a countable discrete amenable group action. For such an action, we introduce entropy tuples in both topological and measure-theoretic settings and…