  The mechanical force from light -- radiation pressure -- provides an
intrinsic nonlinear interaction. Consequently, optomechanical systems near
their steady state, such as the canonical optical spring, can display
non-analytic behavior as a function of external parameters. This
non-analyticity, 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 $\mathbb{Z}_2$ symmetry and derive a free
energy, allowing us to characterize this as an equilibrium phase transition.
