Features of the extension of a statistical measure of complexity to continuous systems

Abstract

We discuss some aspects of the extension to continuous systems of a statistical measure of complexity introduced by López-Ruiz, Mancini, and Calbet [Phys. Lett. A 209, 321 (1995)]. In general, the extension of a magnitude from the discrete to the continuous case is not a trivial process and requires some kind of choice. In the present study, several possibilities appear available. One of them is examined in detail. Some interesting properties desirable for any magnitude of complexity are discovered on this particular extension.

A generalized statistical complexity measure: Applications to quantum systems

“…The importance of a bounded support to obtain this result deserves some longer explanation to be done in a future work, such as it was suggested in [4].…”

“…A continuous version [4] of the measure of complexity C f , the so-called LMC complexity introduced in [3], is defined by…”

Inequalities for phase‐space Rényi entropies

“…They represent the so called disequilibrium or the distance from equilibrium (most probable state). They are fundamental ingredients of the continuous version of the LMC (López-RuizMancini-Calbet) complexity measure is [36].…”

Shannon information, LMC complexity and Rényi entropies: a straightforward approach

“…[7]. When the number of states available for a system is a continuum then the natural representation is a continuous distribution.…”