Propagation of Chaos in Classical and Quantum Kinetics

Abstract

The concept of molecular chaos dates back to Boltzmann [3], who derived the fundamental equation of the kinetic theory of gases from the statistical hypothesis that the molecules of a nonequilibrium gas are in a state of “molecular disorder.” The concept of propagation of molecular chaos is due to Kac [8, 9], who called it “propagation of the Boltzmann property” and used it to derive the homogeneous Boltzmann equation in the infinite-particle limit of certain Markovian gas models (see also [6, 16]). McKean [10, 11] proved the propagation of chaos for systems of interacting diffusions that yield diffusive Vlasov equations in the mean-field limit (see also [4]). See [17] and [12] for two definitive surveys of propagation of chaos and its applications.