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The interaction among the components of a hybrid quantum system is oftenneglected when considering the coupling of these components to an environment.However, if the interaction strength is large, this approximation leads tounphysical predictions, as has been shown for cavity-QED and optomechanicalsystems in the ultrastrong-coupling regime. To deal with these cases, masterequations with dissipators retaining the interaction between these componentshave been derived for the quantum Rabi model and for the standardoptomechanical Hamiltonian. In this article, we go beyond these previousderivations and present a general master equation approach for arbitrary hybridquantum systems interacting with thermal reservoirs. Specifically, our approachcan be applied to describe the dynamics of open hybrid systems with harmonic,quasi-harmonic, and anharmonic transitions. We apply our approach to study theinfluence of temperature on multiphoton vacuum Rabi oscillations in circuitQED. We also analyze the influence of temperature on the conversion ofmechanical energy into photon pairs in an optomechanical system, which has beenrecently described at zero temperature. We compare our results with previousapproaches, finding that these sometimes overestimate decoherence rates andunderstimate excited-state populations.

Dissipation and Thermal Noise in Hybrid Quantum Systems in the Ultrastrong Coupling Regime