Tight uncertainty relations for cycle currents

Understand

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.