Related papers: Local entropy theory and applications
In many complex systems, states and interaction structure coevolve towards a dynamic equilibrium. For the adaptive contact process, we obtain approximate expressions for the degree distributions that characterize the interaction network in…
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…
This paper presents an information theoretic approach to the concept of intelligence in the computational sense. We introduce a probabilistic framework from which computational intelligence is shown to be an entropy minimizing process at…
We use entropy theory as a new tool to study sectional hyperbolic flows in any dimension. We show that for $C^1$ flows, every sectional hyperbolic set $\Lambda$ is entropy expansive, and the topological entropy varies continuously with the…
We study the properties of entanglement in two-dimensional topologically ordered phases of matter. Such phases support anyons, quasiparticles with exotic exchange statistics. The emergent nonlocal state spaces of anyonic systems admit a…
In the current paper we attempt to transfer the notion of the projectional entropy, originally defined for multidimensional subshifts, to the case of actions of amenable groups. The main theorem states that if a system is strongly…
Topological properties play an increasingly important role in future research and technology. This also applies to the field of topological magnetic excitations which has recently become a very active and broad field. In this Perspective…
A diagnostic package is derived from the concept of specific available enthalpy, leading to the definition of a local and complete energy cycle. It is useful to understand the transformations of energy occurring at any particular pressure…
These notes derive a number of technical results on nonlinear contraction theory, a comparatively recent tool for system stability analysis. In particular, they provide new results on the preservation of contraction through system…
We consider impulsive semiflows defined on compact metric spaces and deduce a variational principle. In particular, we generalize the classical notion of topological entropy to our setting of discontinuous semiflows.
The recent developments in fluid/gravity correspondence give a new impulse to the study of fluid dynamics of supersymmetric theories. In that respect, the entropy current formalism requires some modifications in order to be adapted to…
We explore the relationship between Turing completeness and topological entropy of dynamical systems. We first prove that a natural class of Turing machines that we call "branching Turing machines" (which includes most of the known examples…
We review theoretical results obtained recently in the framework of statistical mechanics to study systems with long range forces. This fundamental and methodological study leads us to consider the different domains of applications in a…
Entropic dynamics is a framework for defining dynamical systems that is aligned with the principles of information theory. In an entropic dynamics model for motion on a statistical manifold, we find that the rate of changes for expected…
Motivated by cosmological applications for interacting matters, an extension of the action functional for relativistic fluids is proposed to incorporate the physics of non-adiabatic processes and chemical reactions. The former are…
We develop a systematic approach to the study of independence in topological dynamics with an emphasis on combinatorial methods. One of our principal aims is to combinatorialize the local analysis of topological entropy and related mixing…
We define notions of local topological convergence and local geometric convergence for embedded graphs in $\mathbb{R}^n,$ and study their properties. The former is related to Benjamini-Schramm convergence, and the latter to weak convergence…
We study the directional entropy of the dynamical system associated to a $\Z^2$ configuration in a finite alphabet. We show that under local assumptions on the complexity, either every direction has zero topological entropy or some…
This chapter provides a comprehensive overview of controlling collective behavior in complex systems comprising large ensembles of interacting dynamical agents. Building upon traditional control theory's foundation in individual systems, we…
To test a possible relation between the topological entropy and the Arnold complexity, and to provide a non trivial example of a rational dynamical zeta function, we introduce a two-parameter family of two-dimensional discrete rational…