Quantum and classical systems can consistently be coupled via nonunitary time-irreversible mechanisms. In this paper, we characterize which kind of corresponding dynamics converge in the stationary regime to a thermal hybrid state, that is, a density matrix that maximizes the hybrid arrangement entropy under the constraints of a canonical ensemble. Introducing a detailed balance condition, it is found that a specific subclass of hybrid Lindblad equations fulfill the demanded requirement. The main theoretical results are exemplified through a set of specific dynamics that in addition enlighten how the thermal state of each subsystem in isolation is affected by their mutual coupling. In particular, a Gaussian thermal state could become a bimodal distribution when increasing the interaction strength of a classical subsystem with a quantum two-level subsystem.

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• Open quantum systems
• Quantum stochastic processes
• Quantum thermodynamics
• Markovian processes