11 - Correlations and Linear Response

Summary

This chapter deals with correlation and response functions in equilibrium and in nonequilibrium steady states for a Langevin dynamics. First, the harmonic oscillator in equilibrium is discussed as a paradigmatic case. In the general nonlinear case, it is shown how time-derivatives in correlation functions can be replaced by state variables. The response function is derived within the path integral formalism. It can be expressed by various forms of a correlation function. One particularly transparent version restores the form of the equilibrium fluctuation-dissipation theorem for a nonequilibrium steady state. A second strategy to derive a response function starts with the perturbed Fokker–Plank operator. Causality imposes the Kramers–Kronig relations between the real and imaginary parts of the response function. Through the Harada–Sasa relation, the deviation from the equilibrium form of the fluctuation-dissipation relation can be related to the mean entropy production.