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Equation 12 · Part 2 · The Arrow of Time and the Engine of Evolution

Symbol W

PF(+W)PR(−W)=exp⁡ ⁣(W−ΔFkBT)\frac{P_{\mathrm F}(+W)}{P_{\mathrm R}(-W)} = \exp\!\left(\frac{W - \Delta F}{k_{\mathrm{B}} T}\right)
WW

What this part means

W is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Its job in the formula

W is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

The passage around this formula

…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 PF(+W)PR(−W)=exp⁡ ⁣(W−ΔFkBT)\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 Δ\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 Δ\Delta F , which is the precise, quantitative sense in which a trajectory doing much more work than the…

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A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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