Fluctuations in finite systems: Time reversal symmetry, surface onsager reciprocal relations and fluctuating hydrodynamics

A simple extension of Onsager's regression hypothesis to finite systems is used to derive reciprocal relations between parameters appearing in boundary conditions for the dynamics of second order macroscopic systems. An equivalent Langevin description is constructed; in general it contains surface sources that reflect the dissipative nature of the boundary conditions. Generalized Einstein relations are derived and extensions of the theory to the nonequilibrium domain are discussed. Examples from coupled thermal and mass diffusion, acoustics and hydrodynamics are considered. In particular, a relationship is found between the thermal creep, temperature jump, shear temperature jump and slip coefficients in a one component fluid and the surface noise source correlations are given in terms of these parameters.