Path-Extrema Upper Bounds on Mean Entropy Production (opens in new tab)

Fluctuation relations imply the second-law inequality $\langle\Sigma_T\rangle\ge0$, but path extrema can also constrain how large the mean entropy production can be. For steady-state processes with entropy-production martingale $M_t=e^{-\Sigma_t}$, we show that knowing only the positive running maximum of $\Sigma_t$ gives no improvement over the trivial endpoint bound: rare negative entropy-production excursions can still carry the exponential w...