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Equation 1 · Part 4 · Three Ways to Measure a System That Refuses to Settle Down

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⟨e−βW⟩=e−βΔF\left\langle e^{-\beta W} \right\rangle = e^{-\beta \Delta F}
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What this part means

Capital delta attached to a quantity marks a difference between two values of that quantity; the article’s sign convention determines the order.

Its job in the formula

Capital delta attached to a quantity marks a difference between two values of that quantity; the article’s sign convention determines the order.

The passage around this formula

Because these three frameworks share vocabulary, it is worth being explicit about the one place where a formal expression clarifies rather than decorates the comparison: the Jarzynski equality itself. Written compactly, it states ⟨e−βW⟩=e−βΔF\left\langle e^{-\beta W} \right\rangle = e^{-\beta \Delta F}. where W is the work performed on the system along a single nonequilibrium trajectory, Δ\Delta F is the equilibrium free-energy difference between the initial and final states, and β\beta is inverse temperature. The average on the left is taken over repeated realizations of the same driving protocol, each of which can dissipate a different amount of work due to thermal fluctuations. The identity holds exactly regardless of how fast or far from…

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Learn the underlying idea

Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.

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