Oscillating states of driven Langevin systems in large viscous regime

We employ an appropriate perturbative scheme in the large viscous regime to study oscillating states in driven Langevin systems. We explicitly determine oscillating state distribution of under-damped Brownian particle subjected to thermal, viscous and potential drives to linear order in anharmonic perturbation. We also evaluate various non-equilibrium observables relevant to characterize the oscillating states. We find that the effects of viscous drive on oscillating states are measurable even in the leading order and show that the thermodynamic properties of the system in these states are immensely distinct from those in equilibrium.