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Nonequilibrium heat transport and quantum thermodynamics in quantum light-matter interacting systems have recently attracted increasing attention. Consequently, quantum thermal devices, e.g., heat valve and head diode have been realized. Here, we investigate quantum heat flow in the nonequilibrium anisotropic Dicke model, where an ensemble of qubits collectively interacts with a photon field with anisotropic forms, each component individually interacting with bosonic thermal reservoirs. The quantum dressed master equation (DME) is included to properly study dissipative dynamics of the anisotropic Dicke model, which is able to handle strong qubit-photon coupling within the eigenbasis of the reduced anisotropic Dicke system. Our results demonstrate that anisotropic qubit-photon interactions are crucial for modulating steady-state heat flow, particularly at moderate and strong couplings. We also find that the analytical expressions of heat flows in the thermodynamic limit with limiting anisotropic factors can be used as the upper boundaries for the heat flows in the anisotropic Dicke model with finite qubit numbers. These heat flows exhibit cotunneling microscopic transport processes. Moreover, the large anisotropic factor and nonweak qubit-photon coupling are helpful in achieving the giant thermal rectification effect. We hope these results may deepen the understanding of nonequilibrium heat transport in the anisotropic quantum light-matter interacting systems.
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