  Based on data from the Japan Sea and the North Sea the occurrence of rogue
waves is analyzed by a scale dependent stochastic approach, which interlinks
fluctuations of waves for different spacings. With this approach we are able to
determine a stochastic cascade process, which provides information of the
general multipoint statistics. Furthermore the evolution of single trajectories
in scale, which characterize wave height fluctuations in the surroundings of a
chosen location, can be determined. The explicit knowledge of the stochastic
process enables to assign entropy values to all wave events. We show that for
these entropies the integral fluctuation theorem, a basic law of
non-equilibrium thermodynamics, is valid. This implies that positive and
negative entropy events must occur. Extreme events like rogue waves are
characterized as negative entropy events. The statistics of these entropy
fluctuations changes with the wave state, thus for the Japan Sea the statistics
of the entropies has a more pronounced tail for negative entropy values,
indicating a higher probability of rogue waves.

Atmospheric and Oceanic Physics;Data Analysis, Statistics and Probability