You might want to have a look at the work of Gavin Crook (http://threeplusone.com/gec/), especially the first two chapters of his PhD thesis (to be found on his website) are quite revealing. I'll quickly summarize his main result:
Assume a system is what he calls microscopically reversible, that is, the probability of a trajectory through phase space is related to the probability of the system taking the reverse trajectory by a simple function of the heat (Eq. 1.10 in his thesis). It is initially in equilibrium. Then you drive it out of equilibrium by some (time-reversible) protocol.
Now for an arbitrary function $F$ depending on the path of the system through phase space, it holds that
\begin{equation}
\langle F \rangle_{\mathrm{F}} = \langle \hat F \exp(-\beta W_\mathrm{d})\rangle_{\mathrm R}
\end{equation}
where $\langle \ldots \rangle$ denotes an average over all possible paths the system can take through phase space and F / R denotes the forward / reverse non-equilibrium process. $W_{\mathrm{d}}=W_{\mathrm{tot}} - W_{\mathrm{r}}$ is what he calls dissipative work; it's just the total work minus the minimum amount of work required (reversible work, that is, the free energy difference). $\hat F$ is the time reversal of $F$.
And now it comes: This holds regardless of the strength of the perturbation!
By choosing $F=1$ (or any other constant), one obtains the Jarzynski equality \begin{equation}
\langle \exp(-\beta W) \rangle = \langle \exp(-\beta \Delta F) \rangle
\end{equation}
($\langle \ldots \rangle$ again denotes an average over all possible realizations of the non-equilibrium process) which relates the work performed during a non-equilibrium process to the free energy difference by an equality (!) instead of the inequality resulting from the second law.
With more sophisticated $F$'s one also obtains other relations like the transient fluctuation theorem, the Kawasaki response (which gives you a probability distribution for a non-equilibrium ensemble).
There's a lot more literature; I also recommend the 1997 papers of Christopher Jarzynski (sadly no free access).
At the moment, I'm learning about all these things myself, so the above might not be 100% waterproof explained, but I hope, one gets the idea.
