Universal Scaling Bounds on a Quantum Heat Current

Recently, an extension of thermodynamics to quantum systems, quantum thermodynamics, is intensely studied not only for a fundamental understanding of quantum systems, but also for industrial applications. In particular, for quantum thermodynamic devices such as quantum heat engines that generate a power output, a heat current is an important resource for their quantum-enhanced performances.

In this talk, we present an upper bound on the heat current J, which is universally applicable for an arbitrarily chosen open quantum system. As the first main result, we obtained a scaling bound |J| ≤ Θ(L^3) for an L-particle open quantum system in a limit of large L, and we construct an example that achieves this scaling bound utilizing an L-body interaction induced by the environment. To consider more feasible cases, we impose an additional constraint that the system-environment interaction induces transitions between two system energy eigenstates having a smaller energy difference than a certain value ?E. Then, we obtained another scaling bound |J| ≤ Θ(L^{2+p}) that explicitly depends on ?E = Θ(L^p), and we also found that the so-called superradiance achieves this scaling bound |J| ≤ Θ(L^2) for a case of ?E = Θ(L^0).