Universal Scaling Bounds on a Quantum Heat Current

We derive new bounds on a heat current flowing into a quantum L-particle system coupled with a Markovian environment. By assuming that a system Hamiltonian and a system-environment interaction Hamiltonian are extensive in L, we show that the absolute value of the heat current scales at most as Θ\(L³\) in a limit of large L. Also, we present an example that saturates this bound in terms of scaling: non-interacting particles globally coupled with a thermal bath. However, the construction of such system requires many-body interactions induced by the environment, which may be difficult to realize with the current technology. To consider more feasible cases, we focus on a class of system where any non-diagonal elements of the noise operator (derived from the system-environment interaction Hamiltonian) become zero in the system energy basis, if the energy difference is beyond a certain value ΔE. Then, for ΔE = Θ\(L⁰\), we derive another scaling bound Θ\(L²\) on the absolute value of the heat current, and the so-called superradiance belongs to a class to saturate this bound. Our results are useful to evaluate the best achievable performance of quantum-enhanced thermodynamic devices, which contain far-reaching applications for such as quantum heat engines, quantum refrigerators and quantum batteries.