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. We show that the most prominent of the work theorems, the Jarzynski equality and the Crooks relation,can be applied to the momentum transfer at the air–sea interface using a hierarchy of local models.In the more idealized models, with and without a Coriolis force,the variability is provided from Gaussian white noise which modifies the shear between theatmosphere and the ocean. The dynamics is Gaussian, and the Jarzynski equality and Crooksrelation can be obtained analytically solving stochastic differential equations. The moreinvolved model consists of interacting atmospheric and oceanic boundary layers, where onlythe dependence on the vertical direction is resolved, the turbulence is modeled through standard turbulentmodels and the stochasticity comes from a randomized drag coefficient. It is integratednumerically and can give rise to a non-Gaussian dynamics. Also in this case the Jarzynskiequality allows for calculating a dynamic beta βD of the turbulent fluctuations(the equivalent of the thermodynamic beta β=(kBT)-1 in thermal fluctuations).The Crooks relation gives the βD as a function of the magnitude of the work fluctuations.It is well defined (constant) in the Gaussian models and can show a slight variation in themore involved models. This demonstrates that recent concepts of stochastic thermodynamicsused to study micro-systems subject to thermal fluctuations can further the understandingof geophysical fluid dynamics with turbulent fluctuations.

Jarzynski equality and Crooks relation for local models of air–sea interaction