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We construct a family of ergodic measures on random substitution subshifts (RS-subshifts) associated to a primitive random substitution. In particular, the word frequencies of every finite legal word exist for almost every element of the…
The rate of entropy production by a stochastic process quantifies how far it is from thermodynamic equilibrium. Equivalently, entropy production captures the degree to which detailed balance and time-reversal symmetry are broken. Despite…
We employ an extension of ergodic theory to the random setting to investigate the existence of random periodic solutions of random dynamical systems. Given that a random dynamical system has a dissipative structure, we proved that a random…
Non-reciprocal interactions are present in many systems out of equilibrium. The rate of entropy production is a measure that quantifies the time irreversibility of a system, and thus how far it is from equilibrium. In this work, we…
We introduce the notion of metric entropy for a nonautonomous dynamical system given by a sequence of probability spaces and a sequence of measure-preserving maps between these spaces. This notion generalizes the classical concept of metric…
A recently introduced model of coupled non linear oscillators in a ring is revisited in terms of its information processing capabilities. The use of Lempel-Ziv based entropic measures allows to study thoroughly the complex patterns…
Motivated by studying stochastic systems with non-Gaussian L\'evy noise, spectral properties for a type of linear cocycles are considered. These linear cocycles have countable jump discontinuities in time. A multiplicative ergodic theorem…
In this paper, we investigate a nonparametric approach to provide a recursive estimator of the transition density of a non-stationary piecewise-deterministic Markov process, from only one observation of the path within a long time. In this…
The random local mixture of a family of primitive substitution rules with noble mean inflation multiplier is investigated. This extends the random Fibonacci example that was introduced by Godr\`{e}che and Luck in 1989. We discuss the…
A method for estimating the Shannon differential entropy of multidimensional random variables using independent samples is described. The method is based on decomposing the distribution into a product of the marginal distributions and the…
Entropy in thermodynamics is an extensive quantity, whereas standard methods in statistical mechanics give rise to a non-extensive expression for the entropy. This discrepancy is often seen as a sign that basic formulas of statistical…
An existing dialogue between number theory and dynamical systems is advanced. A combinatorial device gives necessary and sufficient conditions for a sequence of non-negative integers to count the periodic points in a dynamical system. This…
Tempered exponential dichotomy formulates the nonuniform hyperbolicity for random dynamical systems. It was described by admissibility of a pair of function classes defined with Lyapunov norms, For MET-systems (systems satisfying the…
We give computable bounds on the rate of convergence of the transition probabilities to the stationary distribution for a certain class of geometrically ergodic Markov chains. Our results are different from earlier estimates of Meyn and…
We describe a method, using periodic points and determinants, for giving alternative expressions for dynamical quantities (including Lyapunov exponents and Hausdorff dimension of invariant sets) associated to analytic hyperbolic systems.…
It is well known that to estimate the Shannon entropy for symbolic sequences accurately requires a large number of samples. When some aspects of the data are known it is plausible to attempt to use this to more efficiently compute entropy.…
In this paper we study topological entropy and recurrence properties of non-autonomous dynamical system generated by a family of continuous self maps on a compact space X. Specially, we introduce the pseudo-entropy and…
The framework of non-extensive statistical mechanics, proposed by Tsallis, has been used to describe a variety of systems. The non-extensive statistical mechanics is usually introduced in a formal way, using the maximization of entropy. In…
Reservoir computing is a powerful framework for modeling dynamical systems due to its universality and computational efficiency. However, a major challenge is achieving a forecast with accurate long-time statistics, or climate, which is…
Non-equilibrium states of a thermodynamic statistical system are investigated using the thermodynamic parameter of the system lifetime, first-passage time, the time before degeneration of the system under influence of fluctuations.…