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Nascimento, Alexandre Rodrigues do

doi:10.1590/s0100-40422000000300024

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“…Since its introduction in 1948, the Shannon entropy of information theory has seen application in a wide variety of fields. The Shannon entropy is a measure of the uncertainty in the underlying distribution, and in recent years there has been an increased interest and application of information theoretical ideas to study problems in electronic structure and quantum theory …”

Section: Introductionmentioning

confidence: 99%

Information theoretical measures from cumulative and survival densities in quantum systems

Laguna¹,

Sagar²

2017

Int J of Quantum Chemistry

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Entropic uncertainty and statistical correlation measures, based on survival and cumulative densities, are explored in some representative quantum systems. We illustrate how the cumulative residual entropy in the quantum well system recovers the correct classical behavior for larger quantum numbers while the Shannon entropy does not. Two interacting and noninteracting oscillators are used to examine two-particle entropies and their related correlation measures. The joint cumulative residual entropy does distinguish between symmetric and antisymmetric wave functions in interacting systems as the interaction is turned on. The joint Shannon entropy does not distinguish between the symmetries even in the presence of interaction. Conversely, the joint Shannon entropy and joint cumulative residual entropy are both unable to distinguish between the symmetries for certain states of the noninteracting oscillators. As measures of statistical correlation, the mutual information and the cross cumulative residual entropy yield similar behaviors as a function of the strength of the interparticle interaction. K E Y W O R D S correlation measures, cumulative residual entropy, mutual information, quantum systems, Shannon entropy with q(x) the positive probability density defined over the entire range of the real-valued one-dimensional x variable. It should be mentionedthat this definition can be extended to higher dimensions. In this case, the normalization constraint implies that q(x)dx 1, but q(x) is not bounded, thus, it could and does give rise to negative values of the entropy. This is not a serious objection to the differential entropy if one takes care to treat it as a relative measure with the interpretation that given at least two possible systems or two possible states of the system, the entropy measures the response of the density as a delocalization/localization effect. Furthermore, there is no meaning associated with the probability at a certain point, x, in a continuous distribution since what is important is the probability in the element between x and Int J Quantum Chem. 2017;117:e25387.

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Section: Introductionmentioning

confidence: 99%