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Topological entanglement entropy, a measure of the long-ranged entanglement, is related to the degeneracy of the ground state on a higher genus surface. The exact relation depends on the details of the topological theory. We consider a…

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…

In this paper we advance the entropy theory of discrete nonautonomous dynamical systems that was initiated by Kolyada and Snoha in 1996. The first part of the paper is devoted to the measure-theoretic entropy theory of general topological…

Quite often real-world networks can be thought of as being symmetric, in the abstract sense that vertices can be found to have similar or equivalent structural roles. However, traditional measures of symmetry in graphs are based on their…

We establish a connection between barcode entropy and metric entropy. Namely, we show that the barcode entropy bounds the metric entropy from below for a measure from a specific class of invariant measures associated with a pair of…

The form invariance of pseudoadditivity is shown to determine the structure of nonextensive entropies. Nonextensive entropy is defined as the appropriate expectation value of nonextensive information content, similar to the definition of…

We introduce and study a notion of algebraic entropy for self-maps of finite length of Noetherian local rings, and develop its properties. We show that it shares the standard properties of topological entropy. For finite self-maps we…

Salas and Garcia introduced the concept of an extended locally convex space in [D. Salas and S. Tapia-Garcia. Extended seminorms and extended topological vector spaces. Topology and its Applications, 2016] which extends the idea of an…

We introduce the notion of local fibration, a generalization of the notion of fibration which takes into account the presence of Grothendieck topologies on the two categories, and show that the classical results about fibrations lift to…

This paper establishes the minimum entropy principle (MEP) for the relativistic Euler equations with a broad class of equations of state (EOSs) and addresses the challenge of preserving the local version of the discovered MEP in high-order…

Permutation entropy quantifies the diversity of possible orderings of the values a random or deterministic system can take, as Shannon entropy quantifies the diversity of values. We show that the metric and permutation entropy…

Entropy is a measure of self-information which is used to quantify losses. Entropy was developed in thermodynamics, but is also used to compare probabilities based on their deviating information content. Corresponding model uncertainty is…

Two new relative entropy quantities, called the min- and max-relative entropies, are introduced and their properties are investigated. The well-known min- and max- entropies, introduced by Renner, are obtained from these. We define a new…

In this article, I give a definition of topological entropy for random dynamical systems associated to an infinite countable discrete amenable group action. I obtain a variational principle between the topological entropy and measurable…

Twenty years ago Poole et al. (Nature 360, 324, 1992) suggested that the anomalous properties of supercooled water may be caused by a critical point that terminates a line of liquid-liquid separation of lower-density and higher-density…

Phases with distinct thermodynamic properties must differ in their underlying distributions of microscopic structures. While ordered phases are readily distinguished by unit cells and space groups, the local structural basis differentiating…

We prove the entropy conjecture of M. Barge from 1989: for every $r\in [0,\infty]$ there exists a pseudo-arc homeomorphism $h$, whose topological entropy is $r$. Until now all pseudo-arc homeomorphisms with known entropy have had entropy…

We develop a method of obtaining a hierarchy of new higher-order entropies in the context of compressible models with local and non-local diffusion and isentropic pressure. The local viscosity is allowed to degenerate as the density…

Although an intimate relation between entropy and diffusion has been advocated for many years and even seems to have been verified in theory and experiments, a quantitatively reliable study, and any derivation of an algebraic relation…

It is well-known that the relativized variational principle established by Bogenschutz and Kifer connects the fiber topological entropy and fiber measure-theoretic entropy. In context of random dynamical systems, metric mean dimension was…