  We revisit the mechanisms underlying the process of spectral broadening of
incoherent optical waves propagating in nonlinear media on the basis of
nonequilibrium thermodynamic considerations. A simple analysis reveals that a
prerequisite for the existence of a significant spectral broadening of the
waves is that the linear part of the energy (Hamiltonian) has different
contributions of opposite signs. It turns out that, at variance with the
expected soliton turbulence scenario, an increase of the amount of disorder
(incoherence) in the system does not require the generation of a coherent
soliton structure. We illustrate the idea by considering the propagation of two
wave components in an optical fiber with opposite dispersion coefficients. A
wave turbulence approach of the problem reveals that the increase of kinetic
energy in one component is offset by the negative reduction in the other
component, so that the waves exhibit, as a general rule, a virtually unlimited
spectral broadening. More precisely, a self-similar solution of the kinetic
equations reveals that the spectra of the incoherent waves tend to relax toward
a homogeneous distribution in the wake of a front that propagates in frequency
space with a decelerating velocity. We discuss this catastrophic process of
spectral broadening in the light of different important phenomena, in
particular supercontinuum generation, soliton turbulence, wave condensation,
and the runaway motion of mechanical systems composed of positive and negative
masses.
