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

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  • Ván, P.

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.

Suggested Citation

  • Ván, P., 2006. "Unique additive information measures—Boltzmann–Gibbs–Shannon, Fisher and beyond," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(1), pages 28-33.
    • Handle: RePEc:eee:phsmap:v:365:y:2006:i:1:p:28-33
    DOI: 10.1016/j.physa.2006.01.027
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    References listed on IDEAS

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