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Information theoretical measures from cumulative and survival densities in quantum systems
Author(s) -
Laguna Humberto G.,
Sagar Robin P.
Publication year - 2017
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.25387
Subject(s) - residual entropy , statistical physics , joint entropy , total correlation , mutual information , residual , antisymmetric relation , joint quantum entropy , entropy (arrow of time) , mathematics , quantum relative entropy , information theory , quantum discord , correlation , quantum , physics , principle of maximum entropy , quantum mechanics , statistics , configuration entropy , mathematical physics , quantum dynamics , geometry , algorithm
Abstract 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.