subtraction

The passage around this formula

Gavin Crooks sharpened this two years later into a statement about entire probability distributions rather than a single average. If $P_{\mathrm F}(W)$ is the distribution of work values measured over many repetitions of a forward protocol, and $P_{\mathrm R}(W)$ is the distribution measured over the time-reversed protocol run from its own correctly defined reverse-equilibrium starting ensemble, the two distributions are related by $\frac{P_{\mathrm F}(+W)}{P_{\mathrm R}(-W)} = \exp\!\left(\frac{W - \Delta F}{k_{\mathrm{B}} T}\right)$. [ 6 ] . Where W exactly equals $\Delta$ F , the ratio is one and the forward distribution crosses the reflected reverse distribution; away from that point, the ratio grows exponentially in how far W departs from $\Delta$ F , which is the precise,…

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