Cross response in non-equilibrium systems

We study the properties of fluctuations in non-equilibrium systems, focusing our attention on the cross correlations in response to external forcing. Two typical non-equilibrium systems are considered. One is a small coupled set of systems, each of which contacts a different heat bath. The other is an oscillatory system where energy input is balanced with dissipation due to nonlinear friction. Based on the Langevin equations for these systems, we investigate the non-equilibrium statistical properties such as violation of the Clausius relation in the slow change of the parameter, and fluctuations and response around the stationary state. Our main concern is the role played by the probability current.