Symbol P_F
occurs above the fraction bar. The numerator is divided by the entire denominator below it.
Read this term in its guide →Published equation contexts
Why this formula appears here
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…
Read the representative guide
Symbol W
W is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.
Read this term in its guide →Symbol P_R
occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.
Read this term in its guide →Symbol e^(W-Δ F)/k_B T
e^(W-Δ F)/ T is one of the signed contributions combined to compute the quantity on the left.
Read this term in its guide →Denominator: P_R(-W)
The complete quantity below the fraction bar; it must be nonzero for this division.
Read this term in its guide →How to interpret it
With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.
Research cited beside this formula
Published contexts (1)
A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.
Equation 13 · Physics
From Origins to Frontier: A History of Stochastic Thermodynamics and Complex Systems
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.
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…
Equation guide → · Article →