Thermodynamics of Continuous Quantum Measurement in Cavity Optomechanics: Photon-Phonon Heat Fluxes and Quantum-Limited Engine Efficiency

Abstract

Modeling continuous quantum measurement as an explicit thermodynamic process is essential for establishing the operational limits of nanoscale quantum heat engines. In this paper, we develop a comprehensive stochastic thermodynamic framework for a cavity optomechanical system subjected to continuous homodyne monitoring of the optical output. By unraveling the open-system dynamics via a non-linear stochastic master equation, we rigorously partition the measurement-induced energy exchange into an extractable coherent work rate and an irreversible quantum measurement heat flux. We derive the analytical non-equilibrium heat current flowing across the radiation-pressure interface between the optical mode (photons) and the mechanical resonator (phonons). Finally, we demonstrate that continuous measurement acts as an effective non-thermal quantum fuel, establishing a generalized second law that incorporates continuous Shannon information gain from the homodyne photocurrent. We derive the ultimate efficiency at maximum power for a continuous optomechanical engine, demonstrating how quantum measurement backaction sets a fundamental ceiling below the conventional Carnot bound.