Distances in Probability Space and the Statistical Complexity Setup

Entropy

Andres M. Kowalski¹  Maria Teresa Martín¹  Angelo Plastino¹  Osvaldo A. Rosso² 

[1] Instituto de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata (UNLP), C.C. 727, 1900 La Plata, Argentina; E-Mails:;Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Rivadavia 1917, Buenos Aires, Argentina; E-Mail:

关键词: generalized statistical complexity;    disequilibrium;    information theory;    selection of the probability distribution;    semiclassical theories;    quantum chaos;   

DOI  :  10.3390/e13061055

来源: mdpi

【 摘 要 】

Statistical complexity measures (SCM) are the composition of two ingredients: (i) entropies and (ii) distances in probability-space. In consequence, SCMs provide a simultaneous quantification of the randomness and the correlational structures present in the system under study. We address in this review important topics underlying the SCM structure, viz., (a) a good choice of probability metric space and (b) how to assess the best distance-choice, which in this context is called a “disequilibrium” and is denoted with the letter . Since out input data consists of time-series, we also discuss the best way of extracting from the time series a probability distribution P. As an illustration, we show just how these issues affect the description of the classical limit of quantum mechanics.

【 授权许可】

CC BY   
© 2011 by the authors; licensee MDPI, Basel, Switzerland.