COMPLEXITY OF THE MINIMUM ENERGY CONFIGURATIONS

We introduce a method of characterizing the complexity of the minima o f a given function, of N variables, by means of the entropy, S(N), of a measure selected as follows: One chooses an algorithm which computes the minima, and assigns to a single minimum a probability equal to th e (relative) measure of its basin of attraction. The behavior of S(N), for large N, gives a well defined entropy density sigma for the minim a, with respect to the chosen minima-generating law. sigma characteriz es the complexity of the minima in a rather natural way in the framewo rk of information theory, i.e., the number of bits one uses to transmi t one (typical) minimum configuration is similar or equal to N sigma/l n2.