Numerator: 1

The passage around this formula

Christopher Jarzynski’s 1997 equality was the opening result. For a system beginning in thermal equilibrium and then driven away from it by an arbitrarily fast, arbitrarily far-from-equilibrium protocol, the exponential average of the work W performed on it recovers the equilibrium free-energy difference $\Delta$ F between the protocol’s start and end points exactly: $\left\langle e^{-\beta W} \right\rangle = e^{-\beta \Delta F}, \qquad \beta = \frac{1}{k_{\mathrm{B}} T}$. [ 5 ] . The result does not say average work equals $\Delta$ F — dissipation makes the ordinary average of W larger than $\Delta$ F whenever the protocol is not quasistatic — it says a specific nonlinear average of a driven, dissipative, irreversible process reproduces an equilibrium quantity exactly, which is a…

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