  By using recent developments for the Langevin dynamics of spatially
asymmetric systems, we routinely generalize the Onsager-Machlup fluctuation
theory of the second order in time. In this form, it becomes applicable to
fluctuating variables, including hydrodynamic currents, in equilibrium as well
as nonequilibrium steady states. From the solution of the obtained stochastic
equations we derive an analytical expression for the time autocorrelation
function of a general fluctuating quantity. This theoretical result is then
tested in a study of a shear flow by molecular dynamics simulations. The
proposed form of the time autocorrelation function yields an excellent fit to
our computational data for both equilibrium and nonequilibrium steady states.
Unlike the analogous result of the first-order Onsager-Machlup theory, our
expression correctly describes the short-time correlations. Its utility is
demonstrated in an application of the Green-Kubo formula for the transport
coefficient. Curiously, the normalized time autocorrelation function for the
shear flow, which only depends on the deterministic part of the fluctuation
dynamics, appears independent of the external shear force in the linear
nonequilibrium regime.
