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Differential Entropy and Dynamics of Uncertainty

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Abstract

We analyze the functioning of Gibbs-type entropy functionals in the time domain, with emphasis on Shannon and Kullback-Leibler entropies of time-dependent continuous probability distributions. The Shannon entropy validity is extended to probability distributions inferred from L 2(R n) quantum wave packets. In contrast to the von Neumann entropy which simply vanishes on pure states, the differential entropy quantifies the degree of probability (de)localization and its time development. The associated dynamics of the Fisher information functional quantifies nontrivial power transfer processes in the mean, both in dissipative and quantum mechanical cases.

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  1. Institute of Physics, University of Zielona Góra, 65-516, Zielona Góra, Poland

    Piotr Garbaczewski

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  1. Piotr Garbaczewski
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PACS NUMBERS: 05.45.+b, 02.50.-r, 03.65.Ta, 03.67.-a

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Garbaczewski, P. Differential Entropy and Dynamics of Uncertainty. J Stat Phys 123, 315–355 (2006). https://doi.org/10.1007/s10955-006-9058-2

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