Kinetic uncertainty relation on first-passage time for accumulated current
Ken Hiura, Shin‐ichi Sasa
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.
Topics & Concepts
Relation (database)Constraint (computer-aided design)Bounded functionStatistical physicsObservableInterval (graph theory)Stopping timeMathematicsMarkov chainSimple (philosophy)Kinetic energyUpper and lower boundsApplied mathematicsStatisticsPhysicsMathematical analysisComputer scienceCombinatoricsClassical mechanicsQuantum mechanicsEpistemologyPhilosophyGeometryDatabaseAdvanced Thermodynamics and Statistical MechanicsNeural dynamics and brain functionstochastic dynamics and bifurcation