  When two resonantly interacting modes are in contact with a thermostat, their
statistics is exactly Gaussian and the modes are statistically independent
despite strong interaction. Considering noise-driven system, we show that when
one mode is pumped and another dissipates, the statistics (of such cascades) is
never close to Gaussian no matter the interaction/noise relation. One finds
substantial phase correlation in the limit of strong interaction (weak noise).
Surprisingly, for both cascades, the mutual information between modes increases
and entropy further decreases when interaction strength decreases. We use the
model to elucidate the fundamental problem of far-from equilibrium physics:
where the information (entropy deficit) is encoded and how singular measures
form. For an instability-driven system (a laser), even a small added noise
leads to large fluctuations of the relative phase near the stability threshold,
while far from it we show that the conversion into the second harmonic is
weakly affected by noise.
