Equation 3 · Part 2 · Three Ways to Measure a System That Refuses to Settle Down
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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.
Full expression→change→Article meaning
The passage around this formula
where W is the work performed on the system along a single nonequilibrium trajectory, F is the equilibrium free-energy difference between the initial and final states, and 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 equilibrium the driving protocol runs, which is precisely what makes it usable on single-molecule pulling experiments where the process is never quasi-static. Jensen’s inequality applied to the same average recovers the ordinary second-law statement that…
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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