Equation 13 · Part 10 · From Origins to Frontier: A History of Stochastic Thermodynamics and Complex Systems
superscript
superscript
What this part means
A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.
Its job in the formula
A raised mark can be a power or an index. Its position and the surrounding notation determine which.
Full expression→superscript→Article meaning
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…
Learn the underlying idea
An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.
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Sources cited in the surrounding passage
These citations provide research context; check each source for the exact claim it supports.