Unique additive information measures—Boltzmann–Gibbs–Shannon, Fisher and beyond
AbstractIt is proved that the only additive and isotropic information measure that can depend on the probability distribution and also on its first derivative is a linear combination of the Boltzmann–Gibbs–Shannon and Fisher information measures. Power-law equilibrium distributions are found as a result of the interaction of the two terms. The case of second order derivative dependence is investigated and a corresponding additive information measure is given.
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Bibliographic InfoArticle provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.
Volume (Year): 365 (2006)
Issue (Month): 1 ()
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Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/
Fisher information; Non-extensive statistics; Additivity; Schrödinger–Madelung equation;
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