Increasing amount of data allows us today to move from considering low order moments of fluctuating observations to their Probability Density Functions (PDFs). We found a new analytic form of the PDF for two years of sea surface current increments data in the Gulf of Trieste (Northern Adriatic Sea) using the maximum entropy principle twice: in a short timescale and in a longer one. The data for the different wind forcings follow the same analytic PDF form, pointing towards a universal behaviour.

In non-equilibrium statistical mechanics, which describes forced-dissipative systems such as air–sea interaction, there is no universal probability density function (pdf). Some such systems have recently been demonstrated to exhibit a symmetry called a fluctuation theorem (FT), which strongly constrains the shape of the pdf. Using satellite data, the mechanical power input to the ocean by air–sea interaction following or not a FT is questioned. A FT is found to apply over specific ocean regions.

We show that modern concepts of non-equilibrium statistical mechanics can be applied to large-scale environmental fluid dynamics, where fluctuations are not thermal but come from turbulence. The work theorems developed by Jarzynski and Crooks are applied to air–sea interaction. Rather than looking at the average values of thermodynamic variables, their probability density functions are considered, which allows us to replace the inequalities of equilibrium statistical mechanics with equalities.

The input of mechanical power to the ocean due to the surface wind-stress is considered using data from satellites observations. Its dependence on the coarse-graining scale of the atmospheric and oceanic velocity in space and time is determined. The power input is found to increase monotonically with shorter coarse-graining in time. Results show that including the dynamics at scales below a few degrees reduces considerably the power input by air-sea interaction.

The conspicuous feature of the atmosphere–ocean system is the large difference in the masses of the two media. In this respect there is a strong analogy to Brownian motion, with light and fast molecules colliding with heavy and slow Brownian particles. I apply the tools of non-equilibrium statistical mechanics for studying Brownian motion to air–sea interaction.