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Equation 12 · Part 4 · The Arrow of Time and the Engine of Evolution

Symbol Δ 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)
ΔF\Delta F

What this part means

the w exactly equals.

Its job in the formula

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

Where the article explains it

Where W exactly equals Δ\Delta F , the ratio is one and the forward distribution crosses the reflected reverse distribution; away from that point, the ratio grows exponentially in how far W departs from Δ\Delta F , which is the precise, quantitative sense in which a trajectory doing much more work than the equilibrium minimum is exponentially more typical of the forward process than of its reverse.

The passage around this formula

…the distribution measured over the time-reversed protocol run from its own correctly defined reverse-equilibrium starting ensemble, the two distributions are related by 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). [ 6 ] . Where W exactly equals Δ\Delta F , the ratio is one and the forward distribution crosses the reflected reverse distribution; away from that point, the ratio grows exponentially in how far W departs from Δ\Delta F , which is the precise, quantitative sense in which a trajectory doing much more work than the equilibrium…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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