The paper claims that for an underdamped Brownian particle in a spatial temperature gradient, entropy production and extraction rates vanish at zero force while their time-integrated totals stay finite, so a zero rate does not imply equilibrium.
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Thermodynamic Irreversibility in Underdamped Brownian Motion with Spatial Temperature Gradients
The paper claims that for an underdamped Brownian particle in a spatial temperature gradient, entropy production and extraction rates vanish at zero force while their time-integrated totals stay finite, so a zero rate does not imply equilibrium.