# Fundamental Bounds on First Passage Time Fluctuations for Currents

## TL;DR

This paper establishes fundamental bounds linking current fluctuations and first passage time fluctuations in nonequilibrium stochastic systems, extending thermodynamic uncertainty relations through large-deviation theory.

## Contribution

It derives a conjugate uncertainty relation for first passage times and connects current and time fluctuations using large-deviation theory, revealing new bounds and symmetries.

## Key findings

- Derived a conjugate uncertainty relation for first passage times.
- Connected current fluctuations with first passage time fluctuations.
- Transferred known current bounds to first passage time context.

## Abstract

Current is a characteristic feature of nonequilibrium systems. In stochastic systems, these currents exhibit fluctuations constrained by the rate of dissipation in accordance with the recently discovered thermodynamic uncertainty relation. Here, we derive a conjugate uncertainty relationship for the first passage time to accumulate a fixed net current. More generally, we use the tools of large-deviation theory to simply connect current fluctuations and first passage time fluctuations in the limit of long times and large currents. With this connection, previously discovered symmetries and bounds on the large-deviation function for currents are readily transferred to first passage times.