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Equation 14 · Part 12 · The Statistical Mechanics of Irreversibility at Molecular Scale

Denominator: P_mathrm R(-W)

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

What this part means

The complete quantity below the fraction bar; it must be nonzero for this division.

Its job in the formula

PmP_mathrm R(-W) occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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 fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.