Generalized information-entropy measures and Fisher information
| dc.creator | Masi, Marco | |
| dc.date | 2006-11-11 | |
| dc.date | 2006-11-21 | |
| dc.date.accessioned | 2026-07-07T07:31:17Z | |
| dc.date.available | 2026-07-07T07:31:17Z | |
| dc.description | We show how Fisher's information already known particular character as the fundamental information geometric object which plays the role of a metric tensor for a statistical differential manifold, can be derived in a relatively easy manner through the direct application of a generalized logarithm and exponential formalism to generalized information-entropy measures. We shall first shortly describe how the generalization of information-entropy measures naturally comes into being if this formalism is employed and recall how the relation between all the information measures is best understood when described in terms of a particular logarithmic Kolmogorov-Nagumo average. Subsequently, extending Kullback-Leibler's relative entropy to all these measures defined on a manifold of parametrized probability density functions, we obtain the metric which turns out to be the Fisher information matrix elements times a real multiplicative deformation parameter. The metrics independence from the non-extensive character of the system, and its proportionality to the rate of change of the multiplicity under a variation of the statistical probability parameter space, emerges naturally in the frame of this representation. | |
| dc.description | 16 pages, 1 diagram (some references added) | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0611300 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0611300 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/118694 | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Other Condensed Matter | |
| dc.title | Generalized information-entropy measures and Fisher information | |
| dc.type | text |