Nonequilibrium statistical mechanics of shear flow: invariant quantities and currentrelations

Abstract

In modeling nonequilibrium systems one usually starts with a definition of the microscopicdynamics, e.g., in terms of transition rates, and then derives the resulting macroscopicbehavior. We address the inverse question for a class of steady state systems, namelycomplex fluids under continuous shear flow: how does an externally imposed shear currentaffect the microscopic dynamics of the fluid? The answer can be formulated in the form ofinvariant quantities, exact relations for the transition rates in the nonequilibriumsteady state, as discussed in a recent letter (Baule and Evans, 2008 Phys. Rev. Lett. 101 240601). Here, we present a more pedagogical account of the invariant quantitiesand the theory underlying them, known as the nonequilibrium counterpart todetailed balance (NCDB). Furthermore, we investigate the relationship betweenthe transition rates and the shear current in the steady state. We show that afluctuation relation of the Gallavotti–Cohen type holds for systems satisfyingNCDB.