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Equation 14 · Part 1 · The Statistical Mechanics of Irreversibility at Molecular Scale

Symbol P_mathrm 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].
PFP_{\mathrm F}

What this part means

PmP_mathrm F occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Its job in the formula

PmP_mathrm F occurs above the fraction bar. The numerator is divided by the entire denominator below it.

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 subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

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