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

TL;DR

This paper investigates the dynamical responses and the validity of the Jarzynski equality in classical open systems with nonlinear, nonlocal dissipation and state-dependent diffusion, revealing parameter-dependent responses and the nature of work distributions.

Contribution

It introduces a non-Markovian Langevin framework with nonlinear nonlocal dissipation and multiplicative noise, analyzing their effects on system responses and fluctuation relations.

Findings

System responses depend on noise magnitudes and noise relaxation time.

Enhanced fluctuations occur due to nonlinear dissipation and multiplicative noise.

Jarzynski equality holds for ramp forces with Gaussian or non-Gaussian work distributions.

Abstract

We have studied dynamical responses and the Jarzynski equality (JE) of classical open systems described by the generalized Caldeira-Leggett model with the nonlocal system-bath coupling. In the derived non-Markovian Langevin equation, the nonlinear nonlocal dissipative term and state-dependent diffusion term yielding multiplicative colored noise satisfy the fluctuation-dissipation relation. Simulation results for harmonic oscillator systems have shown the following: (a) averaged responses of the system $< x >$ to applied sinusoidal and step forces significantly depend on model parameters of magnitudes of additive and multiplicative noises and the relaxation time of colored noise, although stationary marginal probability distribution functions are independent of them, (b) a combined effect of nonlinear dissipation and multiplicative colored noise induces enhanced fluctuations $< [x-< x>]^2 >$ for an applied sinusoidal force, and (c) the JE holds for an applied ramp force independently of 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 the local and over-damped limits is quite different from the widely adopted phenomenological Markovian Langevin equation subjected to multiplicative noise.