Plasmon decay and nonequilibrium steady states in Josephson junction chains Josephson junction (JJ) chains combine the coherence of superconductivity with the controllability of microwave-frequency circuits, making them a powerful platform for circuit quantum electrodynamics. In this work, we consider a long JJ chain that effectively realizes a multimode cavity with nonlinear dispersion and additional multimode interactions. Individual modes appearing due to the finite size of the chain can be experimentally probed via microwave spectroscopy, both in equilibrium and in driven far-from-equilibrium settings. We study the role of multimode interactions in degrading internal coherence—observable as excess linewidth—in both equilibrium and driven regimes. Focusing on two-into-two mode scattering as the leading relaxation process, we classify the relevant scattering processes and derive their expected temperature- and frequency-scaling under equilibrium conditions. For experimentally relevant parameters, we show that the equilibrium decay rate is dominated by nonresonant processes, however, weakly driving a particular set of modes out of equilibrium enhances resonant scattering, leading to observable signatures in the distribution function and linewidth. Finally, in the strong nonequilibrium regime, we report a crossover to a qualitatively different nonequilibrium steady state. 114 19 American Physical Society application/pdf