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Let $\Gamma$ denote the space of all locally finite subsets (configurations)in $\mathbb R^d$. A stochastic dynamics of binary jumps in continuum is aMarkov process on $\Gamma$ in which pairs of particles simultaneously hop over$\mathbb R^d$. We discuss a non-equilibrium dynamics of binary jumps. We provethe existence of an evolution of correlation functions on a finite timeinterval. We also show that a Vlasov-type mesoscopic scaling for such adynamics leads to a generalized Boltzmann non-linear equation for the particledensity.

Binary jumps in continuum. II. Non-equilibrium process and a Vlasov-type scaling limit