Behavior of the generalized Brownian motion in a parabolic potential: Effect of the field on the bath

The author, in a previous work, solved the generalized Langevin equation of a Brownian particle in a thermal bath whose constituents were composed of noninteracting harmonic oscillators interacting with a parabolic potential. This approach acceptably describes the memory kernel and the frequency-dependent friction coefficient when compared with the molecular dynamic simulation at a constant temperature of methane immersed in water modeled as a Lennard-Jones fluid. In this work, we determine properties, for a field frequency greater than that of the simulation, such as the susceptibility, the timescales of the colored noise correlation function, the average position of the tagged particle, the standard deviation of the position probability density, the time-dependent diffusion coefficient, the system's entropy and production, and the mechanical work generated by an optimum external protocol. The calculations show the system would undergo an atypical-anomalous diffusion because a solvent aggregation process around the particle occurs before it reaches the steady state. This leads to momentary negative entropy production, which vanishes at longer times and is explained in terms of Maxwell's demons and the fulfillment of the second law. Likewise, the optimum driving is no longer linear, and work can be extracted. Furthermore, an alternate method to determine the fluctuation-dissipation theorem is derived. The procedure hasn't appeared in the literature and doesn't appeal to its probability distribution but to simple rules.