Stochastic Thermodynamics of a Linear Optical Cavity Driven On Resonance

Abstract: We present a complete framework of stochastic thermodynamics for a single-mode linear optical cavity driven on resonance. We first show that the steady-state intra-cavity field follows the equilibrium Boltzmann distribution. The effective temperature is given by the noise variance, and the equilibration rate is the dissipation rate. Next we derive expressions for internal energy, work, heat, and free energy of light in a cavity, and formulate the first and second laws of thermodynamics for this system. We then analyze fluctuations in work and heat, and show that they obey universal statistical relations known as fluctuation theorems. Finite time corrections to the fluctuation theorems are also discussed. Additionally, we show that work fluctuations obey the Crook's Fluctuation theorem which is a paradigm for understanding emergent phenomena and estimating free energy differences. The significance of our results is two-fold. On one hand, our work positions optical cavities as a unique platform for fundamental studies of stochastic thermodynamics. On the other hand, our work paves the way for improving the energy efficiency and information processing capabilities of laser-driven optical resonators using a thermodynamics based prescription.