Fig. 2.

Protocol entropy quantifies the diversity of protocols with average dissipation ω. By sampling the distribution equation (Eq. 5) with $t_{\text{obs}}=200$ Monte Carlo sweeps and using various biasing strengths γ, the protocol entropy $S\left(\omega \right)$ was computed using the MBAR method (43). The slope of the protocol entropy at $\omega =\langle \omega \rangle$ gives the strength of the bias necessary to yield mean dissipation $\langle \omega \rangle$. Asymptotic limits for small and large γ are plotted as the dotted and dashed lines, respectively. (Inset) The average dissipation for protocols as a function of the bias γ. Note that a small bias produces most of the achievable dissipation reduction.