value, $W^\dagger$, as the factor $e^{-\beta W}$ has the effect of strongly weighting those work values that are in the far left tail of $\rho$. Explicitly, $$\label{eq:wdag}
W^\dagger = c^{-1}\,\int dW\,g(W)\,W ,$$ where $c = \int dW\,g(W)$. As pointed out by Ritort in the context of a “trajectory thermodynamics” formalism [@Ritort04], the average of $e^{-\beta W}$ is dominated by the region near the peak of the integrand of Eq.\[eq:nwt\_int\], i.e. near $W^\dagger$. I will use the term [*typical*]{} to refer to those realizations whose work values are near the peak of $\rho$, and [*dominant*]{} to refer to those for which the work is near the peak of $g$. Typical realizations are the ones that we ordinarily observe when carrying out the process, while dominant realizations are those rare realizations that contribute the greatest share to the average of $e^{-\beta W}$.

For the process discussed in the previous paragraph, the work parameter $\lambda$ is varied from $A$ to $B$. Following Crooks [@Crooks98], let us also consider a process during which $\lambda$ is manipulated from $B$ to $A$, and let us use the terms [*forward*]{} (F) and [*reverse*]{} (R) to distinguish between the two processes. Specifically, if $\lambda_t^F$ denotes the schedule for 