Equation 4 · How Stochastic Thermodynamics and Complex Systems Actually Work
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where the average is taken over the distribution of work values W from repeated nonequilibrium pulls, 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 ensemble of nonequilibrium runs.
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