  We study thermal radiation from nonlinear ($\chi^{(3)}$) photonic cavities
coupled to external channels and subject to incident monochromatic light. Our
work extends related work on nonlinear mechanical oscillators [Phys. Rev. Lett.
97, 110602 (2006)] to the problem of thermal radiation, demonstrating that
bistability can enhance thermal radiation by orders of magnitude and result in
strong lineshape alternations, including "super-narrow spectral peaks"
occurring at the onset of kinetic phase transitions. We show that when the
cavities are designed so as to have perfect linear absorptivity (rate
matching), such thermally activated transitions can be exploited to
dramatically tune the output power and radiative properties of the cavity,
leading to a kind of Kerr-mediated thermo-optic effect. Finally, we demonstrate
that in certain parameter regimes, the output radiation exhibits Stokes and
anti-Stokes side peaks whose relative magnitudes can be altered by tuning the
internal temperature of the cavity relative to its surroundings, a consequence
of strong correlations and interference between the emitted and reflected
radiation.
