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.
Highlights
(i) entropies and (ii) distances in probability-space
In this review we discuss the role that distances in probability space, as ingredients of statistical complexity measures, play in describing the dynamics of the quantum-classical (QC) transition
In previous works we have shown that, after performing some suitable changes in the definition of the disequilibrium distance, by means of utilization of either Wootters distance [16] or Jensen’s divergence [17], one is in a position to obtain a generalized Statistical complexity measures (SCM) that is: (i) able to grasp essential details of the dynamics
Summary
In this review we discuss the role that distances in probability space, as ingredients of statistical complexity measures, play in describing the dynamics of the quantum-classical (QC) transition. The details of the QC-transition have been elucidated in a series of publications in which the pertinent equations of motion are solved [1,2,3,4]. Our statistical recapitulation covers references [5,6,7] We review here these three works that allow one to ascertain the usefulness of statistical considerations in describing dynamic features. Because (i) usually, statistical approaches are easier to implement than solving equations of motion and (ii) in many cases, they offer the only way of dealing with otherwise intractable problems Why is this of importance? Because (i) usually, statistical approaches are easier to implement than solving equations of motion and (ii) in many cases, they offer the only way of dealing with otherwise intractable problems
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