Thermodynamic uncertainty relation in the overdamped limit with a magnetic Lorentz force

Abstract

In nonequilibrium systems, the relative fluctuation of a current has a universal trade-off relation with the entropy production, called the thermodynamic uncertainty relation (TUR). For systems with broken time reversal symmetry, its violation has been reported in specific models or in the linear response regime. Here, we derive a modified version of the TUR analytically in the overdamped limit for general Langevin dynamics with a magnetic Lorentz force causing time reversal broken. Remarkably, this modified version is simply given by the conventional TUR scaled by the ratio of the reduced effective temperature of the overdamped motion to the reservoir temperature, permitting a violation of the conventional TUR. Without the Lorentz force, this ratio becomes unity and the conventional TUR is restored. We verify our results both analytically and numerically in a specific solvable system.

15 pages

References in corpus (9)

• Thermodynamic uncertainty relation for biomolecular processes
• Proof of the Finite-Time Thermodynamic Uncertainty Relation for Steady-State Currents
• Discrete-time thermodynamic uncertainty relation
• Universal bound on the efficiency of molecular motors
• Unified Approach to Classical Speed Limit and Thermodynamic Uncertainty Relation
• Effect of a magnetic field on the thermodynamic uncertainty relation
• Fluctuation Relation for Heat
• Non-equilibrium driven by an external torque in the presence of a magnetic field
• Finite-time thermodynamic uncertainty relation do not hold for discrete-time Markov process

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