Cyclic Maxwell Demon in granular gas using 2 kinds of spheres with different masses

The problem of Maxwell's demon in granular gas is revisited in the case of a mixture of two particle species. The phase space is found to be 2d. Existence of cyclic orbits, with periodic segregation, is demonstrated by investigating the case of 2 kinds of particles with identical parameters but different masses. At large excitation equi-partition shall be obtained, but convergence towards the steady state is found in spiral. The spiral convergence is imposed due to the rule of kinetic-energy transfer between the two species. It results that the most probable scenario is that the steady state breaks into cyclic orbit at lower amplitude of vibration below a bifurcation threshold. The nature of the bifurcation is not known; it can be critical, subcritical, hypercritical or can exhibit a tri-critical point as varying the control parameters. No conclusion is obtained at very low vibration amplitude: it is guessed two scenarii under further cooling which generates Maxwell's demon and segregation..