Virial-like thermodynamic uncertainty relation in the tight-binding regime

Area of Science:

• Physics
• Statistical Mechanics
• Physical Chemistry

Background:

• Brownian motion describes random particle movement due to thermal energy.
• Entropy production quantifies irreversibility in thermodynamic processes.
• Periodic potentials are fundamental in modeling various physical systems, from solid-state physics to molecular motors.

Purpose of the Study:

• To present a novel methodology for approximating entropy production in Brownian motion within a tilted periodic potential.
• To derive a tighter lower bound for entropy production using a virial-like expansion.
• To establish a simplified validation rule for the tight-binding regime.

Main Methods:

• Applying the thermodynamic uncertainty relation.
• Utilizing a virial-like expansion to derive a lower limit for entropy production.
• Systematic analysis within the tight-binding regime.

Main Results:

• A new approximation for entropy production in Brownian motion was developed.
• A tighter lower limit for entropy production was established, dependent only on drift velocity and diffusion.
• A simple validation rule based on drift and diffusion was proposed for the tight-binding approach.

Conclusions:

• The proposed methodology offers an effective way to approximate entropy production.
• The derived lower limit simplifies the analysis of thermodynamic processes in periodic potentials.
• The findings have implications beyond the tight-binding regime, suggesting broader applicability.