Memory effects on the convergence properties of the Jarzynski equality

In this paper we consider solvable model systems on which finite-time work is done. For the systems and changes in state considered, there is no entropic change and the ensuing work distribution is Gaussian. We focus on the fluctuations in the work for such systems, arising from system-bath interactions and finite system recurrences, and study the resulting effect of dynamical broadening on the corresponding distribution P (e- β0 W). This allows us to describe the dependence of P (e- β0 W) on time and system-bath interactions. From the long-time behavior of the work fluctuations and P (e- β0 W), we clarify both (i) when a stochastic treatment of the dynamics may be legitimately invoked and (ii) how information on the system-bath interaction for stochastic, near-equilibrium, systems may be extracted for such processes where a final temperature is well defined.