Related papers: A brief introduction to sofic entropy theory

Using the definition of entropy of a family of increasing distances on a compact metric set given in [10] we introduce a notion of Finsler entropy for smooth distributions and Stefan-Sussmann foliations. This concept generalizes most of…

We give an elementary introduction to the theory of algebraic and topological quantum groups (in the spirit of S. L. Woronowicz). In particular, we recall the basic facts from Hopf (*-) algebra theory, theory of compact (matrix) quantum…

The R\'enyi entropy is a mathematical generalization of the concept of entropy and it encodes the total information of a system as a funtion of its order parameter $\alpha$. The meaning of the R\'enyi entropy in physics is not completely…

We discuss a quantum Kolmogorov-Sinai entropy defined as the entropy production per unit time resulting from coupling the system to a weak, auxiliary bath. The expressions we obtain are fully quantum, but require that the system is such…

This short expository text is for readers who are confident in basic category theory but know little or nothing about toposes. It is based on some impromptu talks given to a small group of category theorists.

We study the sequence entropy for amenable group actions and investigate systematically spectrum and several mixing concepts via sequence entropy both in measure-theoretic dynamical systems and topological dynamical systems. Moreover, we…

Radical-ion-pair reactions were recently shown to manifest a host of non-trivial quantum effects accounted for by quantum measurement theory. An alternative approach purporting to describe the fundamental quantum dynamics of spin-selective…

We introduce and systematically study linear sofic groups and linear sofic algebras. This generalizes amenable and LEF groups and algebras. We prove that a group is linear sofic if and only if its group algebra is linear sofic. We show that…

This paper introduces the concepts of correlation entropy and local correlation entropy for free semigroup actions on compact metric space, and explores their fundamental properties. Thereafter, we generalize some classical results on…

The microscopic explanation of entropy has been challenged from both experimental and theoretical point of view. The expression of entropy is derived from the first law of thermodynamics indicating that entropy or the second law of…

This article is devoted to showing the product theorem for Bowen's topological entropy.

Let $G$ and $H$ be infinite finitely generated amenable groups. This paper studies two notions of equivalence between actions of such groups on standard Borel probability spaces. They are defined as stable orbit equivalences in which the…

Entropic Dynamics is a framework in which dynamical laws are derived as an application of entropic methods of inference. No underlying action principle is postulated. Instead, the dynamics is driven by entropy subject to the constraints…

A central concept in the connection between physics and information theory is entropy, which represents the amount of information extracted from the system by the observer performing measurements in an experiment. Indeed, Jaynes' principle…

We develop a general method to calculate entropy numbers of standard Sobolev's classes on an arbitrary compact homogeneous Riemannian manifold. Our method is essentially based on a detailed study of geometric characteristics of norms…

We consider (projectively) linearly sofic groups, i.e. groups which can be approximated using (projective) matrices over arbitrary fields, as a generalization of sofic groups. We generalize known results for sofic groups and groups which…

This is a survey, intended both for group theorists and model theorists, concerning the structure of pseudofinite groups, that is, infinite models of the first order theory of finite groups. The focus is on concepts from stability theory…

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…

We prove that a monoid is sofic, in the sense recently introduced by Ceccherini-Silberstein and Coornaert, whenever the J-class of the identity is a sofic group, and the quotients of this group by orbit stabilisers in the rest of the monoid…

The aim of this manuscript is to study some local properties of the topological entropy of a free semigroup action. In order to do that we focus on the set of entropy points of a free semigroup action, show that this set carries the full…