Scalar potentials for light in a cavity

The nonequilibrium dynamics of light in a coherently driven nonlinear cavity resembles the equilibrium Brownian particle scalar potential. This resemblance has been known for decades, but correspondence between two systems never properly assessed. Here we demonstrate that this can be exact, approximate, or break down, depending on driving conditions. For vanishing nonlinearity and on-resonance driving, is exact: dissipation amplitude define potential, follows Boltzmann distribution with an effective temperature defined by noise variance dissipation. potential pertaining to linear fails dramatically and/or off-resonance regimes. However, introduce distinct enabling description light. Our gives reasonably accurate limited regimes bistability, deep bistability where nonconservative forces dominate dynamics. Consequently, motion breaks down. breakdown accompanied qualitative change spectrum small intracavity field fluctuations, reminiscent exceptional point non-Hermitian Hamiltonian. results lay foundations thermodynamic cavities, suggest fundamental overdamped Langevin help assess energetics information processing resonant optical technologies.