Statistical asymmetry:an entropic measure of symmetry

Abstract

This work introduces formally the concept of statistical asymmetry (SA) of a system as an entropic measure of how much it fails to be fully symmetric under a given group of transformations. It is shown that it is able to provide an alternative classification of one-dimensional elementary cellular automata that closely aligns with known others only by measuring symmetry. The behaviour of SA can also be an useful indicator of complex behaviour on two-dimensional discrete processes by following the dynamics of configurations, which is demonstrated in the case of the Geenberg–Hastings model, Conway’s game of life, and the random evolution of discrete square matrices.