Related papers: Entropy Flexibility of Dynamical Systems

In 2007, Ye \& Zhang introduced a version of local topological entropy. Since their entropy function is, as we show under mild conditions, constant for topologically transitive dynamical systems, we propose to adjust the notion in a way…

Chater and MacKay [CM] derived an entropy function of state for exchange economies satisfying a list of axioms, and showed that a change of state of a system of such economies is possible if and only if their total entropy does not…

The time variation of entropy, as an alternative to the variance, is proposed as a measure of the diffusion rate. It is shown that for linear and time-translationally invariant systems having a large-time limit for the density, at large…

Topological entropy is not lower semi-continous: small perturbation of the dynamical system can lead to a collapse of entropy. In this note we show that for some special classes of dynamical systems (geodesic flows, Reeb flows, positive…

We will consider various definitions of topological entropy for multivalued nonautonomous dynamical systems in compact Hausdorff spaces. Some of them can deal with arbitrary multivalued maps, i.e. when no restrictions are imposed on them.…

This is a review on entropy in various fields of mathematics and science. Its scope is to convey a unified vision of the classical as well as some newer entropy notions to a broad audience with an intermediate background in dynamical…

Time-delay systems are, in many ways, a natural set of dynamical systems for natural scientists to study because they form an interface between abstract mathematics and data. However, they are complicated because past states must be…

In arXiv:1801.01238 a variation of Bowen's topological entropy that can be applied to the study of discontinuous semiflows on compact metric spaces was introduced. The main novetly is the use of certain family of pseudosemimetrics…

Here we deconstruct, and then in a reasoned way reconstruct, the concept of "entropy of a system," paying particular attention to where the randomness may be coming from. We start with the core concept of entropy as a COUNT associated with…

The term "overlapping" refers to a certain fairly simple type of piecewise continuous function from the unit interval to itself and also to a fairly simple type of iterated function system (IFS) on the unit interval. A correspondence…

The statistical properties of mostly expanding partially hyperbolic diffeomorphisms have been substantially studied. In this paper, we would like to address the entropy properties of mostly expanding partially hyperbolic diffeomorphisms. We…

In this article, we pay attention to transitive dynamical systems having the shadowing property and the entropy functions are upper semicontinuous. As for these dynamical systems, when we consider ergodic optimization restricted on the…

We present a general definition of entropy in the setting of pre-ordered semigroups, extending the notion of topological entropy. From our definition, we obtain the basic properties exhibited by various entropy-like theories encountered in…

We introduce a novel entropy-related function, \textit{non-repeatability}, designed to capture dynamical behaviors in complex systems. Its normalized form, \textit{mutability}, has been previously applied in statistical physics as a…

The dynamical properties and mechanical functions of amorphous materials are governed by their microscopic structures, particularly the elasticity of the interaction networks, which is generally complicated by structural heterogeneity. This…

According to excess-entropy scaling, dynamic properties of liquids like viscosity and diffusion coefficient are determined by the entropy. This link between dynamics and thermodynamics is increasingly studied and of interest also for…

We study a rich family of robustly non-hyperbolic transitive diffeomorphisms and we show that each ergodic measure is approached by hyperbolic sets in weak$*$-topology and in entropy. For hyperbolic ergodic measures, it is a classical…

We use rigorous non-equilibrium thermodynamic arguments to prove (i) the residual entropy of any system is bounded below by the experimentally (calorimetrically) determined absolute temperature entropy, which itself is bounded below by the…

Co-compact entropy is introduced as an invariant of topological conjugation for perfect mappings defined on any Hausdorff space(compactness and metrizability not necessarily required). This is achieved through the consideration of…

The notion of entropy appears in many fields and this paper is a survey about entropies in several branches of Mathematics. We are mainly concerned with the topological and the algebraic entropy in the context of continuous endomorphisms of…