Extremum complexity in the monodimensional ideal gas: The piecewise uniform density distribution approximation

The extremum complexity distribution is shown to be equivalent to a piecewise uniform distribution in the accessible N-dimensional phase space of a dynamical system. This leads to piecewise exponential functions as one-particle distribution functions. It seems plausible to use these distributions in some systems out of equilibrium, thus greatly simplifying their description. In particular, an isolated ideal monodimensional gas far from equilibrium follows two non-overlapping Gaussian distribution functions. This is demonstrated by numerical simulations. Also, some previous laboratory experiments with granular systems display this kind of distribution.