Thermodynamics of Intersecting Black Branes from Interacting Elementary Branes

If an Einstein-Maxwell-Dilaton system admits the extreme brane solution in which no force works between the parallel branes, the collective motion of nearly parallel branes exhibits the thermodynamical properties which are coincident with those of the corresponding black branes at low energy regime (up to unfixed numerical factors). Hence it may provide the microscopic description of the black branes ($p$-soup proposal). This fact motivates us to test this proposal in the intersecting black branes which have multiple brane charges and/or momentum along the brane direction. We consider the case that the multiple branes satisfy the intersection rule and feel no force when they are static, and find the agreement to the black hole thermodynamics.