Maximum complexity distribution of a monodimensional ideal gas out of equilibrium

The maximum complexity momentum distribution for an isolated monodimensional ideal gas out of equilibrium is derived analytically. In a first approximation, it consists of a double non-overlapping Gaussian distribution. In good agreement with this result, the numerical simulations of a particular isolated monodimensional gas, which is abruptly pushed far from equilibrium, shows the maximum complexity distribution in the decay of the system toward equilibrium.