Equation 11 · The Arrow of Time and the Engine of Evolution
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Symbol P_mathrm R
the distribution measured over the time-reversed protocol run from its own correctly defined reverse-equilibrium starting ensemble, the two distributions are related by.
Symbol W
W is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
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What the article says around this equation
Gavin Crooks sharpened this two years later into a statement about entire probability distributions rather than a single average. If is the distribution of work values measured over many repetitions of a forward protocol, and is the distribution measured over the time-reversed protocol run from its own correctly defined reverse-equilibrium starting ensemble, the two distributions are related by
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 give research context. Read each source to check which claims it supports.
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