Entropy (Jun 2011)

Distances in Probability Space and the Statistical Complexity Setup

  • Montserrat Casas,
  • Osvaldo A. Rosso,
  • Angelo Plastino,
  • Maria Teresa Martín,
  • Andres M. Kowalski

DOI
https://doi.org/10.3390/e13061055
Journal volume & issue
Vol. 13, no. 6
pp. 1055 – 1075

Abstract

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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.

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