  The Heisenberg uncertainty relation, which links the uncertainties of the
position and momentum of a particle, has an important footprint on the quantum
behavior of a physical system. Motivated by this principle, we propose that
thermodynamic currents associated with work, heat, and internal energy are
described by well-defined Hermitian operators; i.e., we associate physical
observables to quantum thermodynamic flows. The observables are defined such
that their expectation values match the average values of the associated
currents. These rates, or currents, differ from their classical counterparts
due to the non-commutativity of the corresponding operators. Using the
Robertson-Schr\"odinger uncertainty relation, we then obtain various
thermodynamic uncertainty relationships between them. In particular, we connect
the fluctuations in heat rate and thermodynamic power with those in internal
energy. We further illustrate this approach by applying it to quantum
batteries, where we derive an energy-power uncertainty relationship and show
how measurements affect the fluctuations.
