Thermodynamic uncertainty relation for Langevin dynamics by scaling time

Area of Science:

• Statistical Mechanics
• Non-equilibrium Thermodynamics
• Stochastic Processes

Background:

• The thermodynamic uncertainty relation (TUR) connects current fluctuations and dissipation in non-equilibrium systems.
• Existing TUR bounds are well-established for overdamped Langevin dynamics.
• Underdamped Langevin dynamics present complexities due to dynamical activity, requiring different analytical approaches.

Purpose of the Study:

• To develop a unified theoretical framework for TUR-like bounds applicable to both overdamped and underdamped Langevin dynamics.
• To explore an alternative perspective using large deviation theory for analyzing current fluctuations.
• To derive and analyze new TUR-like bounds based on scaled current fluctuations.

Main Methods:

• Application of large deviation theory to analyze current fluctuations in Langevin dynamics.
• Development of a unified approach for both overdamped and underdamped systems.
• Time-scaling techniques applied to current fluctuations.

Main Results:

• A general, unified treatment of TUR-like bounds is established for both overdamped and underdamped Langevin dynamics.
• The derived bounds show similarities to, yet distinct differences from, previously known results.
• The large deviation theory approach provides a novel perspective on these bounds.

Conclusions:

• Large deviation theory offers a powerful and unified tool for investigating thermodynamic uncertainty relations in various dynamical regimes.
• The study provides a new set of TUR-like bounds with potential implications for understanding non-equilibrium statistical mechanics.
• The findings highlight the importance of considering system dynamics and fluctuation scaling in bounding thermodynamic quantities.