Nonlinear transport processes: Hydrodynamics

Exact equations of motion for the distribution function and for dynamical variables in systems which are nonlinearly displaced from equilibrium are derived and examined. A projection operator is introduced to resolve these equations into a local equilibrium contribution and correction terms. These are of two types: dissipative and fluctuating and are related by a generalized fluctuation-dissipation theorem. The dissipative terms are essential for a valid description of transport processes. Simplifications are introduced for systems where the local thermodynamic potentials are slowly varying on the scale of the molecular correlation length. This leads to local transport equations. For the hydrodynamical variables these are precisely the Navier-Stokes equations. The entropy production for a system described by such nonlinear equations is positive semidefinite and vanishes if and only if the system is in equilibrium.