Related papers: Infinite ergodic theory and Non-extensive entropie…
We investigate ergodic theory of Poisson suspensions. In the process, we establish close connections between finite and infinite measure preserving ergodic theory. Poisson suspensions thus provide a new approach to infinite measure…
We discuss that the thermodynamics of composite systems with non-additive entropies and additive energies can be equivalently derived considering additive entropies and non-additive energies. The general discussion is illustrated by a…
We introduce methods that allow to derive continuous-time versions of various discrete-time ergodic theorems. We then illustrate these methods by giving simple proofs and refinements of some known results as well as establishing new results…
In this paper we study the ergodic theory and thermodynamic formalism of the geodesic flow on non-compact pinched negatively curved manifolds. We consider two notions of entropy at infinity, the topological and the measure theoretic entropy…
We construct ergodic probability measures with infinite metric entropy for typical continuous maps and homeomorphisms on compact manifolds. We also construct sequences of such measures that converge to a zero-entropy measure.
In this note we identify the distributional limits of non-negative, ergodic stationary processes, showing that all are possible. Consequences for infinite ergodic theory are also explored and new examples of distributionally stable- and…
For infinite measure-theoretic entropy systems, we introduce the notion of measure-theoretic metric mean dimension of invariant measures for different types of measure-theoretic $\epsilon$-entropies, and show that measure-theoretic metric…
We develop operator renewal theory for flows and apply this to infinite ergodic theory. In particular we obtain results on mixing for a large class of infinite measure semiflows. Examples of systems covered by our results include…
The purpose of this note is to argue that degree of nonextensivity as given by Tsallis distribution obtained from maximum entropy principle has a different origin than nonextensivity inferred from pseudo-additive property of Tsallis…
We show that the zeroth law of thermodynamics holds within an alternative version of nonextensive statistical mechanics based on {\it incomplete probability distribution}. The generalized zeroth law leads to a generalized definition of…
A new concept named nonsymmetric entropy which generalizes the concepts of Boltzman's entropy and shannon's entropy, was introduced. Maximal nonsymmetric entropy principle was proven. Some important distribution laws were derived naturally…
Different notions of entropy play a fundamental role in the classical theory of dynamical systems. Unlike many other concepts used to analyze autonomous dynamics, both measure-theoretic and topological entropy can be extended quite…
We present some new nonparametric estimators of entropies and we establish almost sure consistency and central limit Theorems for some of the most important entropies in the discrete case. Our theorical results are validated by simulations.
The definition of nonequilibrium entropy is provided for the general nonequilibrium processes by connecting thermodynamics with statistical physics, and the principle of entropy increment in the nonequilibrium processes is also proved in…
We give some account of investigations for the role of infinite dimensional algebras in time dependent systems.
We form a sequence of oblong matrices by evaluating an integrable vector-valued function along the orbit of an ergodic dynamical system. We obtain an almost sure asymptotic result for the permanents of those matrices. We also give an…
We prove a model theorem for factor maps between ergodic, infinite measure-preserving systems.
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…
The form invariance of pseudoadditivity is shown to determine the structure of nonextensive entropies. Nonextensive entropy is defined as the appropriate expectation value of nonextensive information content, similar to the definition of…
We prove that all entire transcendental entire functions have infinite topological entropy.