Statistical mechanics of systems nonlinearly displaced from equilibrium I

A graphical approach is used to extend the response theory expression for nonequilibrium averages to any arbitrry order in deviations from equilibrium. Various ways in which the perturbation series about equilibrium can be resummed into gradient or Chapman-Enskog like expansions are presented. As a matter of illustration, examples from the hydrodynamics of simple fluids and the motion of a Brownian particle are considered. Specifically the normal stresses, shear dependent viscosity and velocity dependent friction constant are examined.