The hierarchy obtained by integrating the -particle Hamiltonian Liouville equation over successively fewer particle coordinates. Each marginal equation involves the next marginal, so an autonomous one-particle equation requires a closure. For a pair potential, its first equation couples the phase-space distribution function to the two-particle distribution function. Number-normalized factorial marginals and unit-normalized probability marginals have different explicit combinatorial factors.
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The BBGKY hierarchy, named after Boris B. Bogoliubov, A. G. Beme, R. K. Grosse, and V. A. Kolesnikov, is a theoretical framework used in statistical mechanics and mathematical physics for describing the dynamics of a system of interacting particles. The hierarchy provides a set of coupled equations relating the correlation functions of different orders.