Related papers: When do cross-diffusion systems have an entropy st…

A conditional entropic approach is discussed for nonequilibrium complex systems with a weak correlation between spatiotemporally fluctuating quantities on a large time scale. The weak correlation is found to constitute the fluctuation…

We consider some classes of piecewise expanding maps in finite dimensional spaces having invariant probability measures which are absolutely continuous with respect to Lebesgue measure. We derive an entropy formula for such measures and,…

Diffraction methods are used to detect atomic order in solids. While uniquely ergodic systems with pure point diffraction have zero entropy, the relation between diffraction and entropy is not as straightforward in general. In particular,…

According to a previous conjecture, spatial and temporal Lyapunov exponents of chaotic extended systems can be obtained from derivatives of a suitable function: the entropy potential. The validity and the consequences of this hypothesis are…

We consider a cross-diffusion system for which the diffusion of each species is governed solely by the aggregate density through a pressure law of logarithmic or fast diffusion type. The model is set over a one dimensional bounded interval,…

It is well known that the similar universal behavior of infinite-size (bulk) systems of different nature requires the same basic conditions: space dimensionality; number components of order parameter; the type (short- or long-range) of the…

We develop information-theoretic measures of spatial structure and pattern in more than one dimension. As is well known, the entropy density of a two-dimensional configuration can be efficiently and accurately estimated via a converging…

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…

In this paper we analyse a class of nonlinear cross-diffusion systems for two species with local repulsive interactions that exhibit a formal gradient flow structure with respect to the Wasserstein metric. We show that systems where the…

Perturbation theory is used to investigate the evolution of the von Neumann entropy of a subsystem of a bipartite quantum system under the action of a unitary matrix, in the limit where that matrix is close to the unit matrix. The physical…

We study dynamical systems with the property that all the nontrivial factors have infinite topological entropy (or, positive mean dimension). We establish an ``if and only if'' condition for this property among a typical class of dynamical…

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…

We give a notion of entropy for general gemetric structures, which generalizes well-known notions of topological entropy of vector fields and geometric entropy of foliations, and which can also be applied to singular objects, e.g. singular…

Entropy of matter in a very strong gravity depends on cross-sectional area of the container of the system -- is being further bolstered by calculating entropy of a monoatomic gas kept under uniform strong gravity at Newtonian scale. This…

Numerical experiments support the interesting conjecture that statistical methods be applicable not only to fully-chaotic systems, but also at the edge of chaos by using Tsallis' generalizations of the standard exponential and entropy. In…

We revisit a classical continuum model for the diffusion of multiple species with size-exclusion constraint, which leads to a degenerate nonlinear cross-diffusion system. The purpose of this article is twofold: first, it aims at a…

We show analytically that there is anomalous diffusion when the diffusion constant depends on the concentration as a power law with a positive exponent or a negative exponent with absolute value less than one and the initial condition is a…

We define some pointwise properties of topological dynamical systems and give pointwise conditions for such a system possesses positive topological entropy. We give sufficient conditions to obtain positive topological entropy for maps which…

The total entropy production fluctuations are studied in some exactly solvable models. For these systems, the detailed fluctuation theorem holds even in the transient state, provided initially the system is prepared in thermal equilibrium.…

We construct model sets arising from cut and project schemes in Euclidean spaces whose associated Delone dynamical systems have positive toplogical entropy. The construction works both with windows that are proper and with windows that have…