Equation 5 · Part 1 · The Arrow of Time and the Engine of Evolution
Symbol Δ F
What this part means
the w exactly equals.
Its job in the formula
Δ F is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Full expression→Symbol Δ F→Article meaning
Where the article explains it
Where W exactly equals 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 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
Christopher Jarzynski’s 1997 equality was the opening result. For a system beginning in thermal equilibrium and then driven away from it by an arbitrarily fast, arbitrarily far-from-equilibrium protocol, the exponential average of the work W performed on it recovers the equilibrium free-energy difference F between the protocol’s start and end points exactly:
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 article section
- [5] Nonequilibrium Equality for Free Energy Differences ↗
- [6] Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences ↗
- [7] Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies ↗
These citations provide research context; check each source for the exact claim it supports.