Efficiency statistics at all times: Carnot limit at finite power

摘要

We derive the statistics of the efficiency under the assumption thatthermodynamic fluxes fluctuate with normal law, parametrizing it in terms oftime, macroscopic efficiency, and a coupling parameter $\zeta$. It has apeculiar behavior: No moments, one sub- and one super-Carnot maximacorresponding to reverse operating regimes (engine/pump), the most probableefficiency decreasing in time. The limit $\zeta\to 0$ where the Carnot boundcan be saturated gives rise to two extreme situations, one where the machineworks at its macroscopic efficiency, with Carnot limit corresponding to noentropy production, and one where for a transient time scaling like $1/\zeta$microscopic fluctuations are enhanced in such a way that the most probableefficiency approaches Carnot at finite entropy production.