  The wave turbulence theory predicts that a conservative system of nonlinear
waves can exhibit a process of condensation, which originates in the
singularity of the Rayleigh-Jeans equilibrium distribution of classical waves.
Considering light propagation in a multimode fiber, we show that light
condensation is driven by an energy flow toward the higher-order modes, and a
bi-directional redistribution of the wave-action (or power) to the fundamental
mode and to higher-order modes. The analysis of the near-field intensity
distribution provides experimental evidence of this mechanism. The kinetic
equation also shows that the wave-action and energy flows can be inverted
through a thermalization toward a negative temperature equilibrium state, in
which the high-order modes are more populated than low-order modes. In
addition, a Bogoliubov stability analysis reveals that the condensate state is
stable.
