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.
arXiv comment10 pages, 1 figures, shortened
References in corpus (8)
- Non Linear Kinetics underlying Generalized Statistics
- Schrodinger equation from an exact uncertainty principle
- Deformed logarithms and entropies
- A Schroedinger link between non-equilibrium thermodynamics and Fisher information
- Statistical Origin of Quantum Mechanics
- Cosmological Perturbation Theory Using the Schrödinger Equation
- Weakly nonlocal fluid mechanics - the Schrodinger equation
- Quantum mechanics from a Heisenberg-type equality