Nonlinear response. II

Abstract

The nonlinear response theory derived previously is used to discuss the hydrodynamic relaxation of a simple fluid. Closed hydrodynamic equations of motion are given for the macroscopic variables: energy density, momentum density, and particle density. A local equilibrium ensemble is introduced which greatly simplifies the results and emphasizes the importance of the entropic intensive variables. The derived equations are compared with classical irreversible-thermodynamic results. The structure of the equations is similar to the classical equations, there being a natural division between transport terms and convective terms. The theory agrees with the classical results for the convective terms. However, important differences are found in the current coupling in the transport part of the equations. These differences persist in the small-gradient limit. The transport terms are of the form ▿ χαβ (F γ ( r ,t)) ▿F β ( r ,t) where F β ( r ,t) is an intensive variable conjugate with the macroscopic density a β ( r ,t) . Molecular expressions are given for the nonlinear transport coefficients χ αβ ( r ,t)) . The functional dependence of the coefficients on the local intensive variables for systems close to equilibrium is obtained. A discussion of nonlinear generalizations of the Onsager relations is also given. Finally, the entropy production is computed and compared with that predicted by the classical theory.