Network analysis for the steady-state thermodynamic uncertainty relation.

Area of Science:

• Statistical Mechanics
• Network Theory
• Non-equilibrium Physics

Background:

• Master equation describes system dynamics.
• Network analysis and graph theory are powerful tools for studying complex systems.
• Understanding steady-state current noise is crucial in non-equilibrium systems.

Purpose of the Study:

• To estimate the lower bound of steady-state current noise using network analysis.
• To derive a noise lower bound applicable to systems driven to a non-equilibrium steady state.
• To apply this bound to analyze computational time fluctuations and logical irreversibility.

Main Methods:

• Network analysis of systems described by the master equation.
• Utilizing level 2.5 large deviation functions.
• Employing graph theory and mesh currents for noise bound derivation.

Main Results:

• A novel lower bound for steady-state current noise was derived.
• The bound accounts for sojourn time fluctuations across all states.
• Applied to a Brownian computation with reset, the bound captures logical irreversibility, unlike entropy-based bounds.

Conclusions:

• The derived noise lower bound provides a new metric for system fluctuations.
• This approach offers a way to quantify logical irreversibility in computational processes.
• The study advances the understanding of noise in non-equilibrium systems.