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We undertake a thorough analysis of the thermodynamics of the trajectoriesfollowed by a quantum harmonic oscillator coupled to $N$ dissipative baths byusing a new approach to large-deviation theory inspired by phase-space quantumoptics. As an illustrative example, we study the archetypal case of a harmonicoscillator coupled to two thermal baths, allowing for a comparison with theanalogous classical result. In the low-temperature limit, we find a significantquantum suppression in the rate of work exchanged between the system and eachbath. We further show how the presented method is capable of giving analyticalresults even for the case of a driven harmonic oscillator. Based on thatresult, we analyse the laser cooling of the motion of a trapped ion oroptomechanical system, illustrating how the emission statistics can becontrollably altered by the driving force.

Thermodynamics of trajectories of a quantum harmonic oscillator coupled to $N$ baths