Distances in probability space and the statistical complexity setup

• Autores: Kowalski, Andrés Mauricio; Martín, María Teresa; Plastino, Ángelo; Rosso, Osvaldo A.; Casas, Montserrat
• Año de publicación: 2011
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: Ciencias Físicas; Teoría de la Información; Probabilidad; disequilibrium; generalized statistical complexity
• Institución: Comisión de Investigaciones Científicas de la Provincia de Buenos Aires

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.