those in $\zeta_{\rm typ}^R$ (the peak region of ${\cal P}^R$):

\[eq:central\] $$\label{eq:central1}
\zeta_{\rm dom}^F \leftrightarrow \zeta_{\rm typ}^R,$$ where the symbol $\leftrightarrow$ indicates a correspondence through conjugate pairing of trajectories. This is illustrated by the pair of circles in Fig. \[fig:pathSpace\], depicting the peak regions of ${\cal Q}^F$ and ${\cal P}^R$. Similarly, Eq. \[eq:qRpF\] gives us $$\label{eq:central2}
\zeta_{\rm dom}^R \leftrightarrow \zeta_{\rm typ}^F,$$

as illustrated by the ellipses in Fig. \[fig:pathSpace\]. Thus the trajectories typically observed during the reverse process are the conjugate twins of those that dominate $\langle e^{-\beta W}\rangle$ for the forward process (Eq.\[eq:central1\]), and vice-versa (Eq.\[eq:central2\]). This is the central result of this paper.

Let us consider for a moment the special case of a [*cyclic*]{} process, for which the final value of the work parameter is the same as the initial value: $\lambda_0^F = A = B = \lambda_\tau^F$. In this situation $\Delta F = 0$, identically, and Eq. \[eq:nwt0\] becomes $$\label{eq:bk}
\Bigl\langle e^{-\beta W}\Bigr\rangle_F = 1,$$ a result originally derived by Bochkov and Kuzovlev [@BochkovKuzovlev]. Under the additional assumption of a time-symmetric schedule, $\lambda_t^F = \lambda_{\tau-t}^F$, the forward and reverse processes are identical. Thus, for processes that are time-symmetric (and therefore also cyclic), there is no distinction 