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Responses of small open oscillator systems to applied external forces havebeen studied with the use of an exactly solvable classical Caldeira-Leggett(CL) model in which a harmonic oscillator (system) is coupled to finite$N$-body oscillators (bath) with an identical frequency ($\omega_n=\omega_o$for $n=1$ to $N$). We have derived exact expressions for positions, momenta andenergy of the system in nonequilibrium states and for work performed by appliedforces. Detailed study has been made on an analytical method for canonicalaverages of physical quantities over the initial equilibrium state, which ismuch superior than numerical averages commonly adopted in simulations of smallsystems. The calculated energy of the system which is strongly coupled tofinite bath is fluctuating but non-dissipative. It has been shown that theJarzynski equality (JE) is valid in non-dissipative, non-ergodic openoscillator systems regardless of the rate of applied ramp force.

physical review. e, statistical, nonlinear and soft matter physics

Responses to applied forces and the Jarzynski equality in classical  oscillator systems coupled to finite baths: An exactly solvable  non-dissipative non-ergodic model