Kinetic uncertainty relation on first-passage time for accumulated current

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