Unique additive information measures - Boltzmann-Gibbs-Shannon, Fisher and beyond
arXiv:cond-mat/0409255 · doi:10.1016/j.physa.2006.01.027
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.
10 pages, 1 figures, shortened