General nonequilibrium theory of colloid dynamics

A nonequilibrium extension of Onsager's canonical theory of thermal fluctuations is employed to derive a self-consistent theory for the description of the statistical properties of the instantaneous local concentration profile n(r,t) of a colloidal liquid in terms of the coupled time-evolution equations of its mean value (n) over bar (r,t) and of the covariance sigma(r,r';t)equivalent to<(delta n(r,t)delta n(r',t))over bar> of its fluctuations delta n(r,t)=n(r,t)-(n) over bar (r,t). These two coarse-grained equations involve a local mobility function b(r,t) which, in its turn, is written in terms of the memory function of the two-time correlation function C(r,r';t,t')equivalent to<(delta n(r,t)delta n(r',t'))over bar>. For given effective interactions between colloidal particles and applied external fields, the resulting self-consistent theory is aimed at describing the evolution of a strongly correlated colloidal liquid from an initial state with arbitrary mean and covariance (n) over bar (0)(r) and (sigma) over bar (0)(r,r').This theory also provides a general theoretical framework to describe irreversible processes associated with dynamic arrest transitions, such as aging, and the effects of spatial heterogeneities.