‘‘Classical’’ topological entropy is one of the main numerical invariants in topological dynamics on compact spaces. Here, the author’s recent development of a noncommutative generalization of topological entropy, in the natural setting of general *C**‐algebras as the noncommutative counterpart of continuous function algebras on compact spaces, is presented in a slightly modified and improved form. This includes both a survey of earlier results with some important corrections, and also new general results in response to (and inspired by) a more recent counterproposal for a noncommutative topological entropy by Thomsen. Finally, some partially new examples for the calculation of the defined topological entropy are shown. The rather self‐evident physical interpretation in the framework of (operator‐algebraic) quantum statistical mechanics and of ‘‘chaotic’’ quantum dynamical systems is briefly touched upon.

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*U*and

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