## A geometric approach to quantum thermodynamics: from quantum fluctuations to optimal protocols

The average dissipation generated during a slow thermodynamic process can be characterised by introducing a metric on the space of Gibbs states, in such a way that minimally-dissipating protocols correspond to geodesic trajectories. Furthermore, the dissipation is proportional to the work fluctuations for classical systems (which follows from the fluctuation-dissipation relation (FDR)), so that minimising dissipation also minimises fluctuations. In this talk, I will explain how this geometric picture is modified in the quantum regime.