2006/11/11 by Marco Masi, Masi, Marco
Economics, Econometrics and Finance · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Complex Systems and Time Series Analysis #FOS: Physical sciences #Other Condensed Matter (cond-mat.other) #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy #cond-mat.other #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/0611300
16 pages, 1 diagram (some references added)
openalex publication_date 2006/11/11 · arxiv created 2006/11/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.