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Equation 13 · Part 2 · From Origins to Frontier: A History of Stochastic Thermodynamics and Complex Systems

Symbol W

PF(W)PR(−W)=e(W−ΔF)/kBT\frac{P_F(W)}{P_R(-W)} = e^{(W-\Delta F)/k_B T}
WW

What this part means

W is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Its job in the formula

W is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

The passage around this formula

…in “Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences,” published in Physical Review E in 1999 [ 4 ] . Crooks’s relation compares the probability of observing work W in a forward protocol to the probability of observing -W in the corresponding time-reversed protocol: PF(W)PR(−W)=e(W−ΔF)/kBT\frac{P_F(W)}{P_R(-W)} = e^{(W-\Delta F)/k_B T}. The Jarzynski equality follows from the Crooks relation as a special case, and both are instances of a broader family of fluctuation theorems that had been developing since…

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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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