The one-dimensional Boltzmann gas: The ergodic hypothesis and the phase portrait of small systems

The concept of ergodicity and its application to microcanonical systems composed of few particles of different mases are clarified. The distribution functions in position and velocity are theoretically derived and numerically verified. Moreover, we deal with a one-dimensional Boltzmann gas where the order relation (connected to the one dimensionality) brings constraints depending on the two classes of boundary conditions enforced (reflecting, periodic). The numerical simulations on a one-dimensional Boltzmann gas act as real experiments and allow us to play on the constraints to which the system is subjected.