Hard sphere dynamics and the Enskog equation

Low-Density Asymptotic Behavior of Observables of Hard Sphere Fluids

“…and product formula (42), for the limit one-particle marginal distribution function defined by series expansion (37), we finally verify the validity of equality (43). Thus, in the Boltzmann-Grad scaling limit an equivalent approach to the description of the kinetic evolution of hard spheres within the framework of the Cauchy problem of the Boltzmann kinetic equations (39) and (40) is given by the Cauchy problem of the dual Boltzmann hierarchy with hard sphere collisions (25) and (26) for the additivetype marginal observables.…”

“…Furthermore, it was established that for initial states specified by a one-particle distribution function the evolution of additive-type marginal observables is equivalent to a solution of the Boltzmann kinetic equation (39) and the evolution of nonadditive-type marginal observables is equivalent to the property of the propagation of initial chaos for states (43). In other words the Boltzmann-Grad dynamics does not create correlations.…”

“…We note that one more approach to the description of the kinetic evolution of hard spheres is based on the nonMarkovian generalization of the Enskog kinetic equation [43].…”

The Boltzmann–Grad limit of a hard sphere system: analysis of the correlation error

“…In this paper we studied the kinetic theory of expansion (1.14) for a dilute gas of hard spheres. Similar cumulant expansions within the framework of kinetic theory have been considered in [16,5,25,26]. Moreover, they are very familiar in statistical mechanics.…”

Kinetic Equations of Active Soft Matter

“…ðÞ , then for arbitrary t ∈ ℝ series expansion (26) The proof of equality (24) is based on the application of cluster expansions to generating operators (10) of expansions (9) which are dual to the kinetic cluster expansions introduced in paper [35]. Then the adjoint series expansion can be expressed in terms of one-particle distribution function (25) in the form of the functional from the right-hand side of equality (24).…”