Nonequilibrium statistical mechanics for stationary turbulent dispersion

We propose a unified framework to study the turbulent transport problem from the perspective of nonequilibrium statistical mechanics. By combining Krarichnan's turbulence thermalization assumption and Ruelle's recent work on nonequilibrium statistical mechanics settings for fluids, we show that the equation for viscous fluid can be viewed as the non-canonical Hamiltonian system perturbed by different thermostats. This allows an analogy between the viscous fluid and the nonequilibrium heat conduction model where the Fourier modes can be regarded as the ''particles''. With this framework, we reformulate the dispersion of Lagrangian particles in turbulence as a nonequilibrium transport problem. We also derive the first and the second generalized fluctuation-dissipation relations for the Lagrangian particle using respectively the path-integral technique and the Mori-Zwanzig equation. The obtained theoretical results can be used predict the dispersion of the Lagrangian particle in a general nonequilibrium.