Kinetic uncertainty relation on first passage time for accumulated current

TL;DR

This paper derives a kinetic uncertainty relation for the first passage time in Markov processes, showing that the precision of passage time is limited by the mean number of jumps, with applications demonstrating tighter bounds than thermodynamic relations.

Contribution

The paper introduces a new kinetic uncertainty relation for first passage times based on the information inequality at stopping times.

Findings

The precision of first passage time is bounded by the mean number of jumps.

The activity constraint provides a tighter bound than thermodynamic uncertainty relations.

Application to simple systems confirms the theoretical bounds.

Abstract

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.