Related papers: Local variational principle concerning entropy of …

We introduce the algebraic entropy for continuous endomorphisms of locally linearly compact vector spaces over a discrete field, as the natural extension of the algebraic entropy for endomorphisms of discrete vector spaces. We show that the…

Let $(X,T)$ be a topological dynamical system consisting of a compact metric space $X$ and a continuous surjective map $T : X \to X$. By using local entropy theory, we prove that $(X,T)$ has uniformly positive entropy if and only if so does…

Local and category-theoretical entropies associated with an endomorphism of finite length (i.e., with zero-dimensional closed fiber) of a commutative Noetherian local ring are compared. Local entropy is shown to be less than or equal to…

Recently, Li, Li and Zhang introduced the topological pressure for correspondences and measure-theoretic entropy for transition probability kernels. Building thereon, they established a variational principle for correspondences satisfying…

Sofic entropy theory is a generalization of the classical Kolmogorov-Sinai entropy theory to actions of large class of non-amenable groups called sofic groups. This is a short introduction with a guide to the literature.

Let $G$ be a countable discrete sofic group. We define a concept of uniform mixing for measure-preserving $G$-actions and show that it implies completely positive sofic entropy. When $G$ contains an element of infinite order, we use this to…

We explore the measurement problem in the entropic dynamics approach to quantum theory. The dual modes of quantum evolution---either continuous unitary evolution or abrupt wave function collapse during measurement---are unified by virtue of…

We define the topological pressure for any sub-additive potentials of the countable discrete amenable group action and any given open cover. A local variational principle for the topological pressure is established.

This paper derives new bounds on the difference of the entropies of two discrete random variables in terms of the local and total variation distances between their probability mass functions. The derivation of the bounds relies on maximal…

We introduce the notion of weak containment for stationary actions of a countable group and define a natural topology on the space of weak equivalence classes. We prove that Furstenberg entropy is an invariant of weak equivalence, and…

In this paper we introduce the definition of entropy for a partial $\mathbb{Z}$-action. We show that the definition of partial entropy is an extension of the definition of topological entropy for a $\mathbb Z$-action. We also prove that the…

Let $G$ be a topological group, let $\phi$ be a continuous endomorphism of $G$ and let $H$ be a closed $\phi$-invariant subgroup of $G$. We study whether the topological entropy is an additive invariant, that is,…

In this short note we study the entropy for algebraic actions of certain amenable groups. The possible values for this entropy are studied. Various fundamental results about certain classes of amenable groups are reproved using elementary…

We develop a fine-scale local analysis of measure entropy and measure sequence entropy based on combinatorial independence. The concepts of measure IE-tuples and measure IN-tuples are introduced and studied in analogy with their…

We generalize the definition of topological entropy due to Adler, Konheim, and McAndrew \cite{AKM} to set-valued functions from a closed subset $A$ of the interval to closed subsets of the interval. We view these set-valued functions, via…

The purpose of this work is to bound sofic topological entropy of Toeplitz systems over residually finite groups and to prove the Krieger Theorem about attaining arbitrary entropy by the Toeplitz systems. To achieve these results, we…

In this paper, we introduce a new entropy-like invariant, named Hausdorff metric entropy, for finitely generated semigroups acting on compact metric spaces from a set-valued view and study its properties. We establish the relation between…

We introduce a new class of locally compact groups, namely the strongly compactly covered groups, which are the Hausdorff topological groups $G$ such that every element of $G$ is contained in a compact open normal subgroup of $G$. For…

We define a hierarchy of systems with topological completely positive entropy in the context of continuous countable amenable group actions on compact metric spaces. For each countable ordinal we construct a dynamical system on the…

We introduce a new notion of local inverse metric entropy along backward trajectories for ergodic measures preserved by endomorphisms (non-invertible maps) on a compact metric space. A second notion of inverse measure entropy is defined by…