In small-scale thermodynamic devices, fluctuations play an important role (in contrast to standard classical thermodynamics). While close to equilibrium fluctuation-dissipation theorems prescribe how the fluctuations are connected to the desired average output of a device, this is much more difficult to identify far from equilibrium. Interestingly, the thermodynamic properties of a process or of a system constrain fluctuations. This has been studied in terms of thermodynamic and kinetic uncertainty relation (TURs and KURs) – in particular in weakly coupled open quantum systems. However, steady-state thermoelectric heat engines operate typically far from equilibrium and the coupling to contacts can be strong. In this presentation, I will show our recent results on thermodynamic and kinetic constraints on fluctuations. I will focus on implications for quantum heat engines, namely quantum systems subject to temperature differences which can be exploited for power production at small scales.
