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Equation 13 · Part 1 · From Origins to Frontier: A History of Stochastic Thermodynamics and Complex Systems

Symbol P_F

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

What this part means

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

Its job in the formula

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

The passage around this formula

This is a striking claim on its face: it says a quantity defined only for reversible, quasistatic processes — a free energy difference — can be computed from measurements of an irreversible process, no matter how fast or violent the driving, provided enough repetitions are averaged. Two years later, Gavin Crooks derived a closely related and in some respects more general result, the Crooks fluctuation theorem, 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…

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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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