Using precision coefficients of recurrence times and integrated currents to construct a lower bound for the average...

Area of Science:

• Non-equilibrium statistical mechanics
• Physical chemistry
• Biophysics

Background:

• Continuous-time Markov jump processes are fundamental to modeling systems with discrete states and transitions.
• The thermodynamic uncertainty relation (TUR) connects entropy production to current fluctuations, but has limitations.
• Understanding nanoscale systems requires precise measures of efficiency and fluctuations.

Purpose of the Study:

• To develop a generalized uncertainty relation for Markov jump processes.
• To link integrated current precision to recurrence time statistics and effective affinity.
• To explore new avenues for optimizing nanoscale out-of-equilibrium systems.

Main Methods:

• Employing a transition-based formalism for continuous-time Markov jump processes.
• Expressing long-time precision of integrated current using recurrence time precisions.
• Deriving a general inequality incorporating forward and backward recurrence time statistics.

Main Results:

• A novel inequality is established, generalizing the TUR.
• The inequality relates stationary entropy production rate to integrated current fluctuations and recurrence time statistics.
• The derived inequality can be saturated under less restrictive conditions than the TUR.

Conclusions:

• The new inequality provides a more flexible framework for analyzing non-equilibrium systems.
• It offers potential for enhanced design and optimization of nanoscale biological and chemical systems.
• This work advances the understanding of fundamental limits in fluctuating systems.