The classical reactive Boltzmann equation: A derivation in the framework of a stochastic approach to bimolecular reactions

Starting from a classical Liouville equation modified by sink terms, Boltzmann-type equations and a rate constant expression are derived for bimolecular chemical reactions. The treatment uses the stochastic approach proposed by Teramoto and Shigesada which takes the reaction as a stationary Markov process with the numbers of reactants in the system as the only stochastic variables. The obtained equations are compared with the well-known classical reactive Boltzmann equations postulated for calculating non-equilibrium effects in gas-phase reactions. It is shown that these equations are tightly connected with the deterministic behaviour of many-particle systems, which is also the supposition of the existence of reaction order.