Thermokinetic Uncertainty Relations and Dynamical Activities in Quantum Systems

Licentiate thesis, 2026

At the nanoscale, thermodynamics is strongly influenced by fluctuations, quantum effects, and nonequilibrium resources. Consequently, precision becomes an important aspect of performance: even when a device operates efficiently on average, fluctuations in currents, heat flows, or delivered power may hinder it from reliably performing its intended task. This is especially relevant for quantum technologies, which rely on quantum coherence that is sensitive to noise.

This thesis investigates how fluctuations constrain the thermodynamic performance in quantum systems, with a focus on thermodynamic and kinetic uncertainty relations. These relations, originally discovered for classical stochastic systems, limit precision in terms of entropy production and dynamical activity. Extending these bounds to quantum systems is nontrivial, both because the classical bounds may be violated due to quantum effects and because the definition of dynamical activity becomes conceptually subtle.

We tackle these questions by deriving bounds on current noise for coherent quantum transport in the spirit of thermodynamic and kinetic uncertainty relations, together with inference bounds for entropy production relying on current and noise measurements. Moreover, a \emph{partial dynamical activity} is introduced to clarify the relation between different definitions of dynamical activity. In addition, a pragmatic approach is presented where