Linear Response and Complex Diffusivity

This lecture covers martingale-based linear response in periodically driven stochastic systems, effective complex diffusivity, and Nyquist relation. It discusses the analysis of linear response for stochastic systems with time-dependent perturbation and the characterization of perturbed and unperturbed dynamics using martingales. The lecture also explores the Girsanov transform, Einstein relation for reversible diffusions, and the complex mobility matrix. Additionally, it delves into the spectral calculus for diffusions, the reversibility of unperturbed processes, and the variational formula for complex diffusivity. The concept of dissipative systems with weak time-dependent force fields and the mean work per period are also addressed.