Time-dependent response theory and nonequilibrium free-energy relations

The mathematics of time-dependent nonlinear response theory frequently leads to results which although formally exact, are not amenable to experimental application or even to use in computer simulations. Here we give a rigorous derivation of a tractable expression for the thermostatted nonlinear response of classical many body systems to time-dependent dissipative fields. The theory also allows for the concurrent parametric transformation of the system Hamiltonian. Our analysis shows once again the intimate relationship between nonequilibrium free-energy relations such as the Jarzynski equality and nonlinear response theory. We make a few remarks concerning the maximum entropy production approximation.