  Several recent inequalities bound the precision of a current - counting net
number of transitions in a system - by a thermodynamic measure of dissipation.
However, while currents may be defined locally, dissipation is a global
property. Inspired by the fact that ever since Carnot cycles are the unit
elements of thermodynamic processes, we prove similar bounds tailored to cycle
currents - counting net cycle completions - in terms of their conjugate
affinities. We show that these inequalities are stricter than previous ones,
even far from equilibrium, and that they allow to tighten those on transition
currents. We illustrate our results with a simple model and discuss some
technical and conceptual issues related to shifting attention from transition
to cycle observables.
