  We study work fluctuation theorems for oscillators in non-Markovian heat
baths. By calculating the work distribution function for a harmonic oscillator
with motion described by the generalized Langevin equation, the Jarzynski
equality (JE), transient fluctuation theorem (TFT), and Crooks' theorem (CT)
are shown to be exact. In addition to this derivation, numerical simulations of
anharmonic oscillators indicate that the validity of these nonequilibrium
theorems do not depend on the memory of the bath. We find that the JE and the
CT are valid under many oscillator potentials and driving forces whereas the
TFT fails when the driving force is asymmetric in time and the potential is
asymmetric in position.
