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2006•Journal of the London Mathematical SocietyRequires access

RELATIVE ENTROPY, ASYMPTOTIC PAIRS AND CHAOS

Guohua Zhang

Open publisher page 37 citations

Abstract

In this paper, we prove that positive conditional entropy implies the existence of asymptotic pairs and scrambled sets on fibers. Moreover, we introduce the notion of conditional topological entropy for a subset using Bowen's definition of separated and spanning sets, and prove that the conditional topological entropy of a system relative to a factor is the supremum of conditional topological entropy of its scrambled sets on fibers.

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What this paper is about

In this paper, we prove that positive conditional entropy implies the existence of asymptotic pairs and scrambled sets on fibers. Moreover, we introduce the notion of conditional topological entropy for a subset using Bowen's definition of separated and spanning sets, and prove that the conditional topological entropy of a system relative to a factor is the supremum of conditional topological entropy of its scrambled sets on fibers.

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OpenAlex reports 37 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper, we prove that positive conditional entropy implies the existence of asymptotic pairs and scrambled sets on fibers. Moreover, we introduce the notion of conditional topological entropy for a subset using Bowen's definition of separated and spanning sets, and prove that the conditional topological entropy of a system relative to a factor is the supremum of conditional topological entropy of its scrambled sets on fibers.

Key concepts: Mathematics, Topological entropy, Infimum and supremum, Topological entropy in physics, Entropy (arrow of time), Conditional entropy, Statistical physics, Joint quantum entropy

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