Second-order fluctuation theory and time autocorrelation function for currents

Abstract

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.

References in corpus (4)

• Minimal Model of Stochastic Athermal Systems: Origin of Non-Gaussian Noise
• Asymptotic derivation of Langevin-like equation with non-Gaussian noise and its analytical solution
• Asymmetry of steady state current fluctuations in nonequilibrium systems
• The Langevin equation for systems with a preferred spatial direction

Cited by in corpus (7)

• Volterra-series approach to stochastic nonlinear dynamics: linear response of the Van der Pol oscillator driven by white noise
• Statistical physics of inhomogeneous transport: Unification of diffusion laws and inference from first-passage statistics
• A Volterra-series approach to stochastic nonlinear dynamics: The Duffing oscillator driven by white noise
• Dimension reduction of noisy interacting systems
• Effective temperatures for single particle system under dichotomous noise
• Nonequilibrium Langevin dynamics: a demonstration study of shear flow fluctuations in a simple fluid
• Fluctuation theory in space and time: white noise in reaction-diffusion models of morphogenesis