  Responses of small open oscillator systems to applied external forces have
been 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 and
energy of the system in nonequilibrium states and for work performed by applied
forces. Detailed study has been made on an analytical method for canonical
averages of physical quantities over the initial equilibrium state, which is
much superior than numerical averages commonly adopted in simulations of small
systems. The calculated energy of the system which is strongly coupled to
finite bath is fluctuating but non-dissipative. It has been shown that the
Jarzynski equality (JE) is valid in non-dissipative, non-ergodic open
oscillator systems regardless of the rate of applied ramp force.
