Kinetic uncertainty relation on first-passage time for accumulated current

The kinetic uncertainty relation (KUR) is a trade-off relation between the precision of an observable and the mean dynamical activity in a fixed time interval for a time-homogeneous and continuous-time Markov chain. In this Letter, we derive the KUR on the first passage time for the time-integrated current from the information inequality at stopping times. The relation shows that the precision of the first passage time is bounded from above by the mean number of jumps up to that time. We apply our result to simple systems and demonstrate that the activity constraint gives a tighter bound than the thermodynamic uncertainty relation in the regime far from equilibrium.

Automated summary

The kinetic uncertainty relation is a trade-off relation between the precision of an observable and the mean dynamical activity in a fixed time interval for a time-homogeneous and continuous Markov chain. The relation derived in this study shows that the precision of the first passage time is bounded by the mean number of jumps up to that time. The activity constraint provides a tighter bound than the thermodynamic uncertainty relation in systems far from equilibrium.