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Equation 14 · Part 5 · The Statistical Mechanics of Irreversibility at Molecular Scale

Symbol Δ F

PF(W)PR(−W)=exp⁡[β(W−ΔF)].\frac{P_{\mathrm F}(W)}{P_{\mathrm R}(-W)} = \exp\left[\beta(W-\Delta F)\right].
ΔF\Delta F

What this part means

Δ F is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

Δ F is one of the signed contributions combined to compute the quantity on the left.

The passage around this formula

Crooks sharpened the connection by comparing complete forward and reverse work distributions [ 3 ] : PF(W)PR(−W)=exp⁡[β(W−ΔF)]\frac{P_{\mathrm F}(W)}{P_{\mathrm R}(-W)} = \exp\left[\beta(W-\Delta F)\right]. At W=Δ\Delta F , the ratio equals one, so the forward distribution and the reflected reverse distribution cross. This provides both a geometric interpretation and an experimental route to free-energy differences.

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Learn the underlying idea

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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