Related papers: Generalized dynamical entropies in weakly chaotic …
We introduce a high dimensional symplectic map, modeling a large system consisting of weakly interacting chaotic subsystems, as a toy model to analyze the interplay between single-particle chaotic dynamics and particles interactions in…
Whether a system is to be considered complex or not depends on how one searches for correlations. We propose a general scheme for calculation of entropies in lattice systems that has high flexibility in how correlations are successively…
Chaos is an inherently dynamical phenomenon traditionally studied for trajectories that are either permanently erratic or transiently influenced by permanently erratic ones lying on a set of measure zero. The latter gives rise to the final…
Aspects of the dynamical glass transition are considered within a mean field spin glass model. At the dynamical transition the the system condenses in a state of lower entropy. The difference, the information entropy or complexity, is…
Some physical processes, including the intensity fluctuations of a chaotic laser, the detection of single photons, and the Brownian motion of a microscopic particle in a fluid are unpredictable, at least on long timescales. This…
A gas of interacting particles is a paradigmatic example of chaotic systems. It is shown here that even if all but one particle are fixed in generic positions, the excited states of the moving particle are chaotic. They are characterized by…
Consider a chaotic dynamical system generating Brownian motion-like diffusion. Consider a second, non-chaotic system in which all particles localize. Let a particle experience a random combination of both systems by sampling between them in…
We have discussed the Tsallis entropy in finite $N$-unit nonextensive systems, by using the multivariate $q$-Gaussian probability distribution functions (PDFs) derived by the maximum entropy methods with the normal average and the…
The formalism of statistical mechanics can be generalized by starting from more general measures of information than the Shannon entropy and maximizing those subject to suitable constraints. We discuss some of the most important examples of…
We define variational properties for dynamical systems with subexponential complexity, and study these properties in certain specific examples. By computing the value of slow entropy directly, we show that some subshifts are not…
It is shown how, among a class of generalized entropies, the Tsallis entropy can uniquely be identified by the principles of thermodynamics, the concept of stability and the axiomatic foundation.
Tsallis entropy is a useful one-parameter generalization of the standard von Neumann entropy in information theory. We study the variance of Tsallis entropy of bipartite quantum systems in a random pure state. The main result is an exact…
Entropy notions for $\varepsilon$-incremental practical stability and incremental stability of deterministic nonlinear systems under disturbances are introduced. The entropy notions are constructed via a set of points in state space which…
In this paper, we extend the concept of generalized entropy to uniform spaces, allowing computations beyond metrizable settings. We apply this to parabolic dynamics - systems with a unique fixed point uniformly attracting all compact…
We consider the meta-equilibrium state of a composite system made up of independent subsystems satisfying the additive form of external constraints, as recently discussed by Abe [Phys. Rev. E {\bf 63}, 061105 (2001)]. We derive the additive…
This article extends the non-extensive entropy of Tsallis and uses this entropy to model an energy producing system in an absorbing heat bath. This modified non-extensive entropy is superficially identical to the one proposed by Tsallis,…
The increased uncertainty and complexity of nonlinear systems have motivated investigators to consider generalized approaches to defining an entropy function. New insights are achieved by defining the average uncertainty in the probability…
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…
The stochastic entropy generated during the evolution of a system interacting with an environment may be separated into three components, but only two of these have a non-negative mean. The third component of entropy production is…
This is an analysis of the additivity of the entropy of thermodynamical systems with finite heat baths. It is presented an expression for the physical entropy of weakly interacting ergodic systems, and it is shown that it is valid for both…