Thermodynamic uncertainty relation for underdamped Langevin systems driven by a velocity-dependent force

Area of Science:

• Statistical Mechanics
• Non-equilibrium Thermodynamics
• Physical Chemistry

Background:

• The thermodynamic uncertainty relation (TUR) establishes a trade-off between thermodynamic cost and current fluctuations.
• Existing TUR formulations are well-established for discrete-time Markov jump processes and overdamped Langevin dynamics.
• Modifications to TUR are required for underdamped dynamics, particularly for systems with velocity-dependent forces.

Purpose of the Study:

• To develop a generalized thermodynamic uncertainty relation (TUR) applicable to underdamped Langevin dynamics.
• To extend the TUR to systems influenced by velocity-dependent forces, addressing limitations of previous theories.
• To validate the new TUR by applying it to diverse physical systems.

Main Methods:

• Extending the theoretical framework of Vu and Hasegawa (Phys. Rev. E 100, 032130 (2019)).
• Developing a modified TUR specifically for underdamped systems with velocity-dependent forces.
• Applying the derived TUR to analyze trade-off properties in model systems.

Main Results:

• A novel TUR has been derived for underdamped Langevin dynamics with velocity-dependent forces.
• The generalized TUR accurately captures the trade-off between thermodynamic cost and fluctuations.
• The applicability of the new TUR is demonstrated in molecular refrigerators, Brownian dynamics in magnetic fields, and active particle systems.

Conclusions:

• The developed TUR provides a more comprehensive understanding of non-equilibrium thermodynamics in complex systems.
• This work overcomes limitations of previous TURs, enabling analysis of systems with velocity-dependent forces.
• The findings have implications for designing and analyzing nanoscale systems and active matter.