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Equation 14 · Part 8 · The Statistical Mechanics of Irreversibility at Molecular Scale

subtraction

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

What this part means

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

Its job in the formula

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

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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Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.

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