1 A Statistical Measure of Complexity
Abstract
A measure of complexity based on a probabilistic description of physical systems is proposed. This measure incorporates the main features of the intuitive notion of such a magnitude. It can be applied to many physical situations and to different descriptions of a given system. Moreover, the calculation of its value does not require a considerable computational effort in many cases of physical interest. PACS number(s): 05.20.-y, 02.50.+s, 02.70.+d2 On the most basic grounds, an object, a procedure, or system is said to be ”complex ” when it does not match patterns regarded as simple. This sounds rather like an oxymoron but common knowledge tells us what is simple and complex: simplified systems or idealizations are always a starting point to solve scientific problems. The notion of ”complexity ” in physics [1, 2] starts by considering the perfect crystal and the isolated ideal gas as examples of simple models and therefore as systems with zero ”complexity”. Let us briefly recall their main characteristics with ”order”, ”information ” and ”equilibrium”.