Quantum geometry and topological bounds on dissipation in slowly driven systems

In this talk, I will discuss energy dissipation and heating in slowly driven quantum systems. While these effects are often viewed as non-universal and protocol-dependent, I will show that dissipation in nearly adiabatic dynamics is governed by the quantum geometry of the driving protocol. This connection leads to a universal topological lower bound on the energy dissipation rate in certain topological systems. These results reveal a direct link between geometry, topology, and dissipation in open quantum dynamics, and suggest design principles for optimal driving protocols.