Dynamics of a classical hard-sphere gas I. Formal theory

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Abstract
In a microscopic theory for the dynamics of a classical hard sphere fluid a kinetic equation is derived and solved approximately. Besides incorrelated binary collisions which are already included in the generalised Enskog theory, the theory also describes correlated collisions by a mode-coupling approximation. This results in a closed set of non-linear equations for the correlation functions of density, longitudinal and transverse current density and energy density to be solved numerically. The only input required is the density. All existing sum rules of these correlation functions are fulfilled. The theory includes the free particle limit, the exact thermodynamics and a proper hydrodynamic limit yielding corrections to the Enskog transport coefficients.