The mechanical force from light-radiation pressure-provides an intrinsically nonlinear interaction. Consequently, optomechanical systems near their steady state, such as the canonical optical spring, can display nonanalytic behavior as a function of external parameters. This nonanalyticity, a key feature of thermodynamic phase transitions, suggests that there could be an effective thermodynamic description of optomechanical systems. Here we explicitly define the thermodynamic limit for optomechanical systems and derive a set of sufficient constraints on the system parameters as the mechanical system grows large. As an example, we show how these constraints can be satisfied in a system with Z(2) symmetry and derive a free energy, allowing us to characterize this as an equilibrium phase transition.