相关论文: Generalized dynamical entropies in weakly chaotic …

We consider the number of Bowen sets which are necessary to cover a large measure subset of the phase space. This introduce some complexity indicator characterizing different kind of (weakly) chaotic dynamics. Since in many systems its…

We have earlier constructed a generalized entropy concept to show the direction of time in an evolution following from a Markov generator. In such a dynamical system, the entity found changes in a monotonic way starting from any initial…

A powerful tool is developed for the characterization of chaotic signals. The approach is based on the symbolic encoding of time series (according to their ordinal patterns) combined with the ensuing characterization of the corresponding…

Based on the Tsallis entropy, the nonextensive thermodynamic properties are studied as a q-deformation of classical statistical results using only probabilistic methods and straightforward calculations. It is shown that the constant in the…

This paper presents an {\it ab initio} derivation of the expression given by irreversible thermodynamics for the rate of entropy production for different classes of diffusive processes. The first class are Lorentz gases, where…

We study, using information quantifiers, the dynamics generated by a special Hamiltonian that gives a detailed account of the interaction between a classical and a quantum system. The associated, very rich dynamics displays periodicity,…

We present a sampling-based trajectory optimization method derived from the maximum entropy formulation of Differential Dynamic Programming with Tsallis entropy. This method is a generalization of the legacy work with Shannon entropy, which…

A diagonal entropy, which depends only on the diagonal elements of the system's density matrix in the energy representation, has been recently introduced as the proper definition of thermodynamic entropy in out-of-equilibrium quantum…

Starting from the geometrical interpretation of the R\'enyi entropy, we introduce further extensive generalizations and study their properties. In particular, we found the probability distribution function obtained by the MaxEnt principle…

The chaotical dynamics is studied in different Friedmann-Robertson- Walker cosmological models with scalar (inflaton) field and hydrodynamical matter. The topological entropy is calculated for some particular cases. Suggested scheme can be…

We propose a new way to measure the balance between freedom and coherence in a dynamical system and a new measure of its internal variability. Based on the concept of entropy and ideas from neuroscience and information theory, we define…

Symbolic dynamics has proven to be an invaluable tool in analyzing the mechanisms that lead to unpredictability and random behavior in nonlinear dynamical systems. Surprisingly, a discrete partition of continuous state space can produce a…

A three-component dynamic system with influence of pumping and nonlinear dissipation describing a quantum cavity electrodynamic device is studied. Different dynamical regimes are investigated in terms of divergent trajectories approaches…

We develop the framework of classical Observational entropy, which is a mathematically rigorous and precise framework for non-equilibrium thermodynamics, explicitly defined in terms of a set of observables. Observational entropy can be seen…

The Tsallis entropy barrier or the roundness barrier based dynamic stochastic resonance mechanisms are put forward and simulated. The systems with various Tsallis q values exhibit the effects of emergence as a result of the noise-induced…

We consider the problem of defining free energy and other thermodynamic functions when the entropy is given as a general function of the probablity distribution, including that for non extensive forms. We find that the free energy, which is…

In this letter, we study the limit behavior of the evolution of Tsallis entropy in self-gravitating systems. The study is carried out under two different situations, drawing the same conclusion. No matter in the energy transfer process or…

A family of nonlinear ordinary differential equations with arbitrary order is obtained by using nonextensive concepts related to the Tsallis entropy. Applications of these equations are given here. In particular, a connection between…

We investigate the cumulative Tsallis entropy, an information measure recently introduced as a cumulative version of the classical Tsallis differential entropy, which is itself a generalization of the Boltzmann-Gibbs statistics. This…

A new approach to non-extensive thermodynamical systems with non-additive energy and entropy is proposed. The main idea of the paper is based on the statistical matching of the thermodynamical systems with the additive multi-step Markov…