Fundamental Bounds on First Passage Time Fluctuations for Currents.

Area of Science:

• Non-equilibrium thermodynamics
• Stochastic systems
• Statistical mechanics

Background:

• Currents are fundamental to non-equilibrium systems, exhibiting fluctuations.
• The thermodynamic uncertainty relation constrains these current fluctuations by dissipation.
• Existing research focuses on current fluctuations, with less attention on first passage times.

Purpose of the Study:

• To derive a conjugate uncertainty relation for first passage time in stochastic systems.
• To establish a general connection between current and first passage time fluctuations.
• To extend known results on current fluctuations to first passage time phenomena.

Main Methods:

• Utilized tools from large-deviation theory.
• Derived a novel conjugate uncertainty relationship.
• Analyzed systems in the limit of long times and large currents.

Main Results:

• A new uncertainty relation for first passage time to accumulate a fixed net current was derived.
• A general connection was established between fluctuations of system currents and their first passage times.
• Symmetries and bounds for large-deviation functions of currents were successfully transferred to first passage times.

Conclusions:

• The study provides a unified framework for understanding fluctuations in both currents and first passage times.
• This work extends the applicability of thermodynamic uncertainty relations to first passage time statistics.
• The findings offer new insights into the behavior of stochastic systems far from equilibrium.