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Equation 14 · Part 4 · The Statistical Mechanics of Irreversibility at Molecular Scale

Symbol β

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

What this part means

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

Its job in the formula

β 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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A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the surrounding passage

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