Schematically, the Liouville equation gives us the time evolution for the whole N -particle system in the form D f N = 0 , which expresses an incompressible flow of the probability density in phase space. We then define the reduced distribution functions incrementally by integrating out another particle's degrees of freedom f s ∼ ∼ ∫ ∫ f s + 1 . An equation in the BBGKY hierarchy tells us that the time evolution for such a f s is consequently given by a Liouville-like equation, but with a correction term that represents force-influence of the N − − s suppressed particles