  We calculate the damping rate of Josephson plasmons due to thermally excited
quasiparticles in a nonequilibrium steady state. It is known that the
experimentally observed dependence of the damping rate on the phase difference
behaves in the opposite way to that of theory. It is shown that this problem
can be solved by calculating the damping rate by incorporating changes in the
electronic state at the resonant frequency. When the phase difference is large,
the broadening of the one-particle state is large due to the presence of a dc
current and brings about the effective thermalization, so that the
nonequilibrium correction becomes small. Conversely, when the phase difference
is small, the nonequilibrium correction becomes large and causes a smaller
damping rate due to a reduction in the effective temperature. This dependence
of the nonequilibrium correction on the phase difference results in a damping
rate that is consistent with experimental results.
