Nonlinear Transport Coefficient from Large Deviation Functions

Nonlinear response occurs naturally when a strong external perturbation takes a system far from equilibrium. While linear response can be directly related to equilibrium fluctuations, nonlinear response is difficult to predict in a general and efficient way. In this talk, we illustrate a method to compute arbitrarily high order transport coefficients of stochastic systems from derivatives of a large deviation function. We explore a selection of examples ranging from a single Brownian ratchet to thermal rectification in a mass-graded Fermi-Pasta-Ulam chain. Our method not only derives transport coefficients with relatively small statistical error, but also can be useful in studying mechanism by which nonlinear behavior arises.