Unique additive information measures—Boltzmann–Gibbs–Shannon, Fisher and beyond

P. Ván

Physica A: Statistical Mechanics and its Applications, 2006, vol. 365, issue 1, 28-33

Abstract: It 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.

Keywords: Fisher information; Non-extensive statistics; Additivity; Schrödinger–Madelung equation (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:365:y:2006:i:1:p:28-33

DOI: 10.1016/j.physa.2006.01.027

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