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

Distances in Probability Space and the Statistical Complexity Setup

1 Instituto de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata (UNLP), C.C. 727, 1900 La Plata, Argentina 2 Comisión de Investigaciones Científicas (CICPBA), Calle 526 entre 10 y 11, 1900 La Plata, Buenos Aires, Argentina 3 Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Rivadavia 1917, Buenos Aires, Argentina 4 Departamento de Física, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, Av. Antônio Carlos, 6627, Campus Pampulha, 31270-901 Belo Horizonte, MG, Brazil 5 Chaos & Biology Group, Instituto de Cálculo, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón II, Ciudad Universitaria, 1428 Ciudad Autónoma de Buenos Aires, Argentina 6 IFISC-CSIC, Universitat de les Illes Balears, 07122 Palma de Mallorca, Spain
* Author to whom correspondence should be addressed.
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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