Distances in probability space and the statistical complexity setup

• Autores: Kowalski, A.M.; Martín, M.T.; Plastino, A.; Rosso, O.A.; Casas, M.
• Año de publicación: 2011
• Idioma: inglés
• Tipo de recurso: artículo
• Fuente: Entropy 2011;13(6):1055-1075
• Materia: Disequilibrium; Generalized statistical complexity; Information theory; Quantum chaos; Selection of the probability distribution; Semiclassical theories
• Institución: Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales

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