Effect of a magnetic field on the thermodynamic uncertainty relation

Abstract

The thermodynamic uncertainty relation provides a universal lower bound on the product of entropy production and the fluctuations of any current. While proven for Markov dynamics on a discrete set of states and for overdamped Langevin dynamics, its status for underdamped dynamics is still open. We consider a two-dimensional harmonically confined charged particle in a magnetic field under the action of an external torque. We show analytically that, depending on the sign of the magnetic field, the thermodynamic uncertainty relation does not hold for the currents associated with work and heat. A strong magnetic field can effectively localize the particle with concomitant bounded fluctuations and low dissipation. Numerical results for a three-dimensional variant and for further currents suggest that the existence of such a bound depends crucially on the specific current.

arXiv comment8 pages, 4 figures (v2) Sec.III is revised. Fig.1 is updated

References in corpus (25)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Thermodynamic uncertainty relation for biomolecular processes
• Dissipation bounds all steady-state current fluctuations
• Universal trade-off between power, efficiency, and constancy in steady-state heat engines
• Proof of the Finite-Time Thermodynamic Uncertainty Relation for Steady-State Currents
• Universal bounds on current fluctuations
• Finite-time generalization of the thermodynamic uncertainty relation
• Current fluctuations and transport efficiency for general Langevin systems
• Introduction to dynamical large deviations of Markov processes
• Discrete-time thermodynamic uncertainty relation
• Generic Properties of Stochastic Entropy Production
• Inferring dissipation from current fluctuations
• Thermodynamic Bounds on Precision in Ballistic Multi-Terminal Transport
• Unified thermodynamic uncertainty relations in linear response
• Multidimensional thermodynamic uncertainty relations
• The Brownian gyrator: a minimal heat engine on the nano-scale
• Tightening the uncertainty principle for stochastic currents
• Stochastic thermodynamics: From principles to the cost of precision
• Experimental Realization of a Minimal Microscopic Heat Engine
• Bounds on current fluctuations in periodically driven systems
• A generalization of the thermodynamic uncertainty relation to periodically driven systems
• Electrical Autonomous Brownian Gyrator
• Large Deviation Function for a Driven Underdamped Particle in a Periodic Potential
• Stochastic thermodynamics for delayed Langevin systems
• Non-equilibrium fluctuations for linear diffusion dynamics

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