Unique additive information measures - Boltzmann-Gibbs-Shannon, Fisher and beyond

Details Unique additive information measures - Boltzmann-Gibbs-Shannon, Fisher and beyond Unique additive information measures - Boltzmann-Gibbs-Shannon, Fisher and beyond

2004-09-10

arxiv.org/abs/cond-mat/0409255v4

Physica A, 2006, V365, p28-33

Physics

Condensed Matter

Statistical Mechanics

10 pages, 1 figures, shortened

Scientific paper

10.1016/j.physa.2006.01.027

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.

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