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.
| Original language | English |
|---|---|
| Pages (from-to) | 28-33 |
| Number of pages | 6 |
| Journal | Physica A: Statistical Mechanics and its Applications |
| Volume | 365 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - jún. 1 2006 |
Fingerprint
ASJC Scopus subject areas
- Mathematical Physics
- Statistical and Nonlinear Physics
Cite this
Unique additive information measures-Boltzmann-Gibbs-Shannon, Fisher and beyond. / Ván, P.
In: Physica A: Statistical Mechanics and its Applications, Vol. 365, No. 1, 01.06.2006, p. 28-33.Research output: Article
}
TY - JOUR
T1 - Unique additive information measures-Boltzmann-Gibbs-Shannon, Fisher and beyond
AU - Ván, P.
PY - 2006/6/1
Y1 - 2006/6/1
N2 - 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.
AB - 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.
KW - Additivity
KW - Fisher information
KW - Non-extensive statistics
KW - Schrödinger-Madelung equation
UR - http://www.scopus.com/inward/record.url?scp=33645972263&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33645972263&partnerID=8YFLogxK
U2 - 10.1016/j.physa.2006.01.027
DO - 10.1016/j.physa.2006.01.027
M3 - Article
AN - SCOPUS:33645972263
VL - 365
SP - 28
EP - 33
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
SN - 0378-4371
IS - 1
ER -