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)
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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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