Entropy 2011, 13(6), 1055-1075; doi:10.3390/e13061055

Distances in Probability Space and the Statistical Complexity Setup

1,2email, 1,3email, 1,4,* email, 3,4,5 and 6email
Received: 11 April 2011; Accepted: 27 May 2011 / Published: 3 June 2011
(This article belongs to the Special Issue Distance in Information and Statistical Physics Volume 2)
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract: 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 Q. Q, indeed the crucial SCM ingredient, is cast in terms of an associated distance D. 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.
Keywords: generalized statistical complexity; disequilibrium; information theory; selection of the probability distribution; semiclassical theories; quantum chaos
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MDPI and ACS Style

Kowalski, A.M.; Martín, M.T.; Plastino, A.; Rosso, O.A.; Casas, M. Distances in Probability Space and the Statistical Complexity Setup. Entropy 2011, 13, 1055-1075.

AMA Style

Kowalski AM, Martín MT, Plastino A, Rosso OA, Casas M. Distances in Probability Space and the Statistical Complexity Setup. Entropy. 2011; 13(6):1055-1075.

Chicago/Turabian Style

Kowalski, Andres M.; Martín, Maria Teresa; Plastino, Angelo; Rosso, Osvaldo A.; Casas, Montserrat. 2011. "Distances in Probability Space and the Statistical Complexity Setup." Entropy 13, no. 6: 1055-1075.

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