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Equation 2 · Part 6 · How Stochastic Thermodynamics and Complex Systems Actually Work

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e−ΔF/kBT=⟨e−W/kBT⟩e^{-\Delta F / k_B T} = \left\langle e^{-W/k_B T} \right\rangle
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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.

The passage around this formula

It is not. The Jarzynski equality states e−ΔF/kBT=⟨e−W/kBT⟩e^{-\Delta F / k_B T} = \left\langle e^{-W/k_B T} \right\rangle. where the average is taken over the distribution of work values W from repeated nonequilibrium pulls, kBk_B is Boltzmann’s constant and T the bath temperature [ 1 ] . The identity holds regardless of how fast or violent the pulling protocol is, provided the system starts each repetition in thermal equilibrium. This is the mechanism, stated plainly: because the exponential average is dominated by the rare trajectories that violate the second law locally by absorbing more work back than expected, those rare low-work outcomes carry disproportionate weight, and that weighting is exactly what reconstructs the equilibrium quantity from an…

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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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