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Continuing our inquiry into the conditions when fluctuation-dissipationrelations (FDR) may appear in the context of nonequilibrium dynamics of openquantum systems (over and beyond the conventional FDR from linear responsetheory) we turn to nonGaussian systems and consider this issue for ananharmonic oscillator interacting with a scalar quantum field bath. We presentthe general {nonperturbative} expressions for the rate of energy (power)exchange between the anharmonic oscillator and the thermal bath. For the casesthat a stable final equilibrium state exists, and the nonstationary componentsof the two-point functions of the anharmonic oscillator have negligiblecontributions to the evaluation of the power balance, we can shownonperturbatively that equilibration implies an FDR for the anharmonicoscillator. We then use a weakly anharmonic oscillator as an example toillustrate that those two assumptions indeed are satisfied according to ourfirst-order perturbative results: that the net energy exchange vanishes afterrelaxation in the open system dynamics and an equilibrium state exists at latetimes.

Fluctuation-Dissipation Relation from the Nonequilibrium Dynamics of a Nonlinear Open Quantum System