  We study the effect of non-equilibrium quasiparticles on the operation of a
superconducting device (a qubit or a resonator), including heating of the
quasiparticles by the device operation. Focusing on the competition between
heating via low-frequency photon absorption and cooling via photon and phonon
emission, we obtain a remarkably simple non-thermal stationary solution of the
kinetic equation for the quasiparticle distribution function. We estimate the
influence of quasiparticles on relaxation and excitation rates for transmon
qubits, and relate our findings to recent experiments.
