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Kinetic uncertainty relation on first-passage time for accumulated current
1Department of Physics, Kyoto University, Kyoto 606-8502, Japan.
Physical Review. E
|June 17, 2021
Summary
We derived a kinetic uncertainty relation for first passage time, showing precision is limited by the number of system jumps. This provides a tighter bound than existing relations, especially far from equilibrium.
Area of Science:
- Statistical Mechanics
- Information Theory
- Stochastic Processes
Background:
- The kinetic uncertainty relation (KUR) quantifies trade-offs between measurement precision and dynamical activity in Markov chains.
- Existing KURs apply to fixed time intervals and homogeneous systems.
Purpose of the Study:
- Derive a KUR for first passage time (FPT) of integrated current.
- Establish a bound on FPT precision based on system activity.
Main Methods:
- Utilized information inequalities at stopping times.
- Applied the derived KUR to simple systems.
Main Results:
- Established a KUR for FPT, bounding precision by the mean number of jumps.
- Demonstrated tighter bounds compared to the thermodynamic uncertainty relation in non-equilibrium regimes.
Conclusions:
- The derived KUR offers a more refined constraint on FPT precision.
- This finding has implications for understanding non-equilibrium systems and information processing.
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