Response Theory: Trajectory-Based Approach

This lecture by the instructor delves into response theory using a trajectory-based approach, focusing on nonequilibrium statistical mechanics. The content covers the construction of new relations between diffusion and friction, the generation of negative differential mobility, and the influence of time-symmetric dynamical activity. Through examples and derivations, the lecture explores the implications of linear response around equilibrium and nonequilibrium systems, emphasizing the importance of dynamical activity and entropy flux. The discussion extends to the interpretation of entropy, dynamical activity, and the role of kinetics in coupling with reservoirs. The lecture concludes with open questions regarding the Girsanov theorem and the kinetic extension of thermodynamic analogues in dynamical systems.