Temperature-driven irreversible generalized Langevin equation can capture the nonequilibrium dynamics of two dissipated coupled oscillators

Kawai and Komatsuzaki [J. Chem. Phys. 134, 114523 (2011)] recently derived the nonequilibrium generalized Langevin equation (GLE) for a nonstationary system using the projection operator technique. In the limit when the environment is slowly changing (that is, a quasi-equilibrium bath), it should reduce to the irreversible GLE approach (iGLE) [J. Chem. Phys. 111, 7701 (1999)]. Kawai and Komatsuzaki, however, found that the driven harmonic oscillator, an example of a nonequilibrium system does not obey the iGLE presumably because it did not quite satisfy the limiting conditions of the latter. Notwithstanding the lack of a massive quasi-equilibrium bath (one of the conditions under which the iGLE had been derived earlier), we found that the temperature-driven iGLE (T-iGLE) [J. Chem. Phys. 126, 244506 (2007)] can reproduce the nonequilibrium dynamics of a driven dissipated pair of harmonic oscillators. It requires a choice of the function representing the coupling between the oscillator coordinate and the bath and shows that the T-iGLE representation is consistent with the projection operator formalism if only dominant bath modes are taken into account. Moreover, we also show that the more readily applicable phenomenological iGLE model is recoverable from the Kawai and Komatsuzaki model beyond the adiabatic limit used in the original T-iGLE theory.