Related papers: Local entropy theory and applications
In this paper we report that notions of topological protection can be applied to stationary configurations that are driven far from equilibrium by active, dissipative processes. We show this for physically two disparate cases : stochastic…
We consider the category of partially observable dynamical systems, to which the entropy theory of dynamical systems extends functorially. This leads us to introduce quotient-topological entropy. We discuss the structure that emerges. We…
Conventional Non-equilibrium Thermodynamics is mainly concerned with systems in local equilibrium and their entropy production, due to the irreversible processes which take place in these systems. In this paper fluids will be considered in…
We review some of the recent progress on the study of entropy of entanglement in many-body quantum systems. Emphasis is placed on the scaling properties of entropy for one-dimensional multi-partite models at quantum phase transitions and,…
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.
In order to provide a formally correct thermodynamical description of inhomogeneous fluids valid on all length scales down to the classical limit we postulate that all extensive quantities have locally extensive analogues. We derive local…
We introduce the concept of inflation word entropy for random substitutions with a constant and primitive substitution matrix. Previous calculations of the topological entropy of such systems implicitly used this concept and established…
In the study of ad hoc sensor networks, clustering plays an important role in energy conservation therefore analyzing the mechanics of such topology can be helpful to make logistic decisions .Using the theory of complex network the…
This is a paper in Analytic Topology.
The concept of entropy rate for a dynamical process on a graph is introduced. We study diffusion processes where the node degrees are used as a local information by the random walkers. We describe analitically and numerically how the degree…
In this paper we develop a systematic theory of compact operator semigroups on locally convex vector spaces. In particular we prove new and generalized versions of the mean ergodic theorem and apply them to different notions of mean…
This is an account of one man's view of the current perspective of theory of topological groups. We survey some recent developments which are, from our viewpoint, indicative of the future directions, concentrating on actions of topological…
The concept of the theory of continuous groups of transformations has attracted the attention of applied mathematicians and engineers to solve many physical problems in the engineering sciences. Three applications are presented in this…
In this master's thesis, we rigorously develop two frameworks of relational composition of systems using tools from category theory. The first framework addresses port-Hamiltonian systems, which are dynamical systems whose dynamics are…
We review the physical meaning and mathematical implementation of the condition of local detailed balance for a class of nonequilibrium mesoscopic processes. A central concept is that of fluctuating entropy flux for which the steady average…
We consider lattice gas automata where the lack of semi-detailed balance results from node occupation redistribution ruled by distant configurations; such models with nonlocal interactions are interesting because they exhibit non-ideal gas…
The inherent structure approach, wherein thermodynamic and structural changes in glass forming liquids are analyzed in terms of local potential energy minima that the liquid samples, has recently been applied extensively to the study of…
This is a review article on the distributions of entry and return times in dynamical systems which discusses recent results for systems of positive entropy.
A continuous cohomology theory for topological quandles is introduced, and compared to the algebraic theories. Extensions of topological quandles are studied with respect to continuous 2-cocycles, and used to show the differences in second…
We study the dependence of the topological entropy of piecewise monotonic maps with holes under perturbations, for example sliding a hole of fixed size at uniform speed or expanding a hole with uniform expansion. We show that under suitable…