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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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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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e−ΔF/kBTe^{-\Delta F / k_B T}

Symbol e^-Δ F / k_B T

e−e^-Δ F / kBk_B T is part of the quantity the equation computes from the expression on the right.

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e−W/kBTe^{-W/k_B T}

Symbol e^-W/k_B T

e−e^-W/kBk_B T is one of the signed contributions combined to compute the quantity on the left.

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Published contexts (1)

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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

Equation 2 · Physics

How Stochastic Thermodynamics and Complex Systems Actually Work

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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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