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dc.contributor.authorNelson, Kenric P.en_US
dc.contributor.authorUmarov, Sabir R.en_US
dc.contributor.authorKon, Mark A.en_US
dc.date.accessioned2019-11-06T14:37:49Z
dc.date.available2019-11-06T14:37:49Z
dc.date.issued2017-02-15
dc.identifier.citationKenric P Nelson, Sabir R Umarov, Mark A Kon. 2017. "On the average uncertainty for systems with nonlinear coupling." Physica A: Statistical Mechanics and its Applications, Volume 468, pp. 30 - 43. https://doi.org/10.1016/j.physa.2016.09.046
dc.identifier.issn0378-4371
dc.identifier.urihttps://hdl.handle.net/2144/38441
dc.description.abstractThe increased uncertainty and complexity of nonlinear systems have motivated investigators to consider generalized approaches to defining an entropy function. New insights are achieved by defining the average uncertainty in the probability domain as a transformation of entropy functions. The Shannon entropy when transformed to the probability domain is the weighted geometric mean of the probabilities. For the exponential and Gaussian distributions, we show that the weighted geometric mean of the distribution is equal to the density of the distribution at the location plus the scale (i.e. at the width of the distribution). The average uncertainty is generalized via the weighted generalized mean, in which the moment is a function of the nonlinear source. Both the Rényi and Tsallis entropies transform to this definition of the generalized average uncertainty in the probability domain. For the generalized Pareto and Student’s t-distributions, which are the maximum entropy distributions for these generalized entropies, the appropriate weighted generalized mean also equals the density of the distribution at the location plus scale. A coupled entropy function is proposed, which is equal to the normalized Tsallis entropy divided by one plus the coupling.en_US
dc.format.extent30 - 43en_US
dc.publisherElsevieren_US
dc.relation.ispartofPhysica A: Statistical Mechanics and its Applications
dc.subjectPhysical sciencesen_US
dc.subjectPhysicsen_US
dc.subjectComplex systemsen_US
dc.subjectNonlinear couplingen_US
dc.subjectNon-additive entropyen_US
dc.subjectNonextensive statistical mechanicsen_US
dc.subjectStatisticsen_US
dc.subjectFluids & plasmasen_US
dc.subjectMathematical physicsen_US
dc.subjectQuantum physicsen_US
dc.titleOn the average uncertainty for systems with nonlinear couplingen_US
dc.typeArticleen_US
dc.description.versionAccepted manuscripten_US
dc.identifier.doi10.1016/j.physa.2016.09.046
pubs.elements-sourcemanual-entryen_US
pubs.notesEmbargo: Not knownen_US
pubs.organisational-groupBoston Universityen_US
pubs.organisational-groupBoston University, College of Arts & Sciencesen_US
pubs.organisational-groupBoston University, College of Arts & Sciences, Department of Mathematics & Statisticsen_US
pubs.organisational-groupBoston University, College of Engineeringen_US
pubs.organisational-groupBoston University, College of Engineering, Department of Electrical & Computer Engineeringen_US
pubs.publication-statusPublisheden_US
dc.identifier.orcid0000-0001-5902-9412 (Kon, Mark A)
dc.identifier.mycv61328


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