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Generalized entropy of induced zero-entropy systems

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Given a compact metric space $X$ and a continuous map $T: X \to X$, the induced hyperspace map $T_\mathcal{K}$ acts on the hyperspace $\mathcal{K}(X)$ of nonempty closed sets of $X$, and the measure-induced map $T_*$ acts on the space of probability measures $\mathcal{M}(X)$.
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Assessment of thermohydraulic performance and entropy generation in an evacuated tube solar collector employing pure water and nanofluids as working fluids. [PDF]

open access: yesHeliyon
López-Núñez OA   +5 more
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Generalized entropies

Mathematical Notes, 1996
The purpose of this note is to study Renyi entropies from the ergodic theory viewpoint. Applications of the Renyi entropies to dynamical systems seem to have first appeared in the physical literature in order to define chaotic behaviour numerically. Here the authors present an elegant and mathematically rigorous approach to Renyi entropies.
Verbitskij, E. A., Takens, F.
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GENERAL ENTROPY OF GENERAL MEASURES

International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2002
The concept of entropy is an important part of the theory of additive measures. In this paper, a definition of entropy is introduced for general (not necessarily additive) measures as the infinum of the Shannon entropies of "subordinate" additive measures. Several properties of the general entropy are discussed and proved.
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