Linear response of nonequilibrium stochastic dynamics

Transport coefficients relate an external forcing applied to a system to its response in terms of a current. I will first recall, in a hopefully pedagogical way, how these properties are defined for typical ergodic stochastic dynamics such as Langevin dynamics. I will then present approaches to estimate them using both linear response theory and Green-Kubo formulas. I will provide elements of numerical analysis, both to characterize the bias arising from finite time integration and the use of finite timesteps, and to quantify the statistical error in terms of variance. I will in particular present a newly developed method based on Girsanov's change-of-measure theory in the linear response regime, as introduced in works on sensitivity analysis (joint work with Petr Plechac and Ting Wang, arXiv preprint 1910.02479).