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Equation 12 · Part 1 · The Arrow of Time and the Engine of Evolution

Symbol P_mathrm F

PF(+W)PR(−W)=exp⁡ ⁣(W−ΔFkBT)\frac{P_{\mathrm F}(+W)}{P_{\mathrm R}(-W)} = \exp\!\left(\frac{W - \Delta F}{k_{\mathrm{B}} T}\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

Gavin Crooks sharpened this two years later into a statement about entire probability distributions rather than a single average. If PF(W)P_{\mathrm F}(W) is the distribution of work values measured over many repetitions of a forward protocol, and PR(W)P_{\mathrm R}(W) is the distribution measured over the time-reversed protocol run from its own correctly defined reverse-equilibrium starting ensemble, the two distributions are related by…

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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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