Kinetic uncertainty relation on first passage time for accumulated current

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.

arXiv comment5 + 3 pages

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• Speed limit for a highly irreversible process and tight finite-time Landauer's bound
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• Quality of the Thermodynamic Uncertainty Relation for Fast and Slow Driving
• Precision bounds for multiple currents in open quantum systems
• SLD Fisher information for kinetic uncertainty relations
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• Entropy of Sharp Restart
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• Full counting statistics and first-passage times in quantum Markovian processes: Ensemble relations, metastability, and fluctuation theorems
• Inverse thermodynamic uncertainty relation and entropy production
• Finite-time dynamics of an entanglement engine: current, fluctuations and kinetic uncertainty relations
• Concentration of Empirical First-Passage Times