Quantum geometry and bounds on dissipation in slowly driven quantum systems

We show that energy dissipation in slowly-driven, Markovian quantum systems at low temperature is linked to the geometry of the driving protocol through the quantum (or Fubini-Study) metric. Utilizing these findings, we establish lower bounds on dissipation rates in two-tone protocols, such as those employed for topological frequency conversion. Notably, in appropriate limits these bounds are only determined by the topology of the protocol and an effective quality factor of the system-bath coupling. Our results bridge topological and geometric phenomena with energy dissipation in open quantum systems, and further provide design principles for optimal driving protocols.