Renormalized Kinetic Theory of Classical Fluids in and out of Equilibrium

Abstract We present a theory for the construction of renormalized kinetic equations to describe the dynamics of classical systems of particles in or out of equilibrium. A closed, self-consistent set of evolution equations is derived for the single-particle phase-space distri-bution function f, the correlation function C = 〈δf δf 〉, the retarded and advanced density response functions χR,A = δf/δφ to an external potential φ, and the associated memory functions R,A,C. The basis of the theory is an effective action functional of external potentials φ that contains all information about the dynamical properties of the system. In particular, its functional derivatives generate successively the single-particle phase-space density f and all the correlation and density response functions, which are coupled through an infinite hierarchy of evolution equations. Traditional renormalization techniques (involv-ing Legendre transform and vertex functions) are then used to perform the closure of the hierarchy through memory functions. The latter satisfy functional equations that can be used to devise systematic approximations that automatically imply the conservation laws of mass, momentum and energy. The present formulation can be equally regarded as (i) a generalization to dynamical problems of the density functional theory of fluids in equi