Segregation in hard-sphere mixtures under gravity. An extension of Edwards approach with two thermodynamical parameters

We study segregation patterns in a hard-sphere binary model under gravity subject to sequences of taps. We discuss the appearance of the Brazil nut effect (where large particles move up) and the reverse Brazil nut effects in the stationary states reached by tap dynamics. In particular, we show that the stationary state depends only on two thermodynamical quantities: the gravitational energy of the first and of the second species, and not on the sample history. To describe the properties of the system, we generalize Edwards approach by introducing a canonical distribution characterized by two configurational temperatures, conjugate to the energies of the two species. This is supported by Monte Carlo calculations showing that the average of several quantities over the tap dynamics and over such distribution coincide. The segregation problem can then be understood as an equilibrium statistical-mechanics problem with two control parameters.