Thermodynamic limits for optomechanical systems with conservative potentials

TL;DR

This paper establishes the thermodynamic limit for optomechanical systems with nonlinear radiation pressure interactions, deriving conditions for phase transitions and providing a framework for their thermodynamic description.

Contribution

It explicitly defines the thermodynamic limit for optomechanical systems and derives constraints for phase transition analysis in large systems.

Findings

Derived a set of constraints for the thermodynamic limit.

Established a free energy framework for phase transition characterization.

Demonstrated the approach with a symmetric optomechanical system.

Abstract

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.