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We have studied dynamical responses and the Jarzynski equality (JE) ofclassical open systems described by the generalized Caldeira-Leggett model withthe nonlocal system-bath coupling. In the derived non-Markovian Langevinequation, the nonlinear nonlocal dissipative term and state-dependent diffusionterm yielding multiplicative colored noise satisfy the fluctuation-dissipationrelation. Simulation results for harmonic oscillator systems have shown thefollowing: (a) averaged responses of the system $< x >$ to applied sinusoidaland step forces significantly depend on model parameters of magnitudes ofadditive and multiplicative noises and the relaxation time of colored noise,although stationary marginal probability distribution functions are independentof them, (b) a combined effect of nonlinear dissipation and multiplicativecolored noise induces enhanced fluctuations $< [x-< x>]^2 >$ for an appliedsinusoidal force, and (c) the JE holds for an applied ramp force independentlyof the model parameters with a work distribution function which is (symmetric)Gaussian and asymmetric non-Gaussian for additive and multiplicative noises,respectively. It has been shown that the non-Markovian Langevin equation in thelocal and over-damped limits is quite different from the widely adoptedphenomenological Markovian Langevin equation subjected to multiplicative noise.

Classical open systems with nonlinear nonlocal dissipation and state-dependent diffusion: Dynamical responses and the Jarzynski equality