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.

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

References in corpus (6)

• Thermodynamic uncertainty relation for biomolecular processes
• Proof of the Finite-Time Thermodynamic Uncertainty Relation for Steady-State Currents
• Discrete-time thermodynamic uncertainty relation
• The Brownian gyrator: a minimal heat engine on the nano-scale
• Experimental Realization of a Minimal Microscopic Heat Engine
• Stochastic thermodynamics for delayed Langevin systems

Cited by in corpus (18)

• Operationally accessible bounds on fluctuations and entropy production in periodically driven systems
• Classical pendulum clocks break the thermodynamic uncertainty relation
• Geometric decomposition of entropy production into excess, housekeeping and coupling parts
• Inertial effects on the Brownian gyrator
• Absence and recovery of cost-precision tradeoff relations in quantum transport
• Exploring quantum thermodynamics with NMR
• Thermodynamic Uncertainty Relation in Interacting Many-Body Systems
• Precision bound and optimal control in periodically modulated continuous quantum thermal machines
• Thermodynamic uncertainty relations for systems with broken time reversal symmetry: the case of superconducting hybrid systems
• Quality of the Thermodynamic Uncertainty Relation for Fast and Slow Driving
• The Dance of Odd-Diffusive Particles: A Fourier Approach
• The origin of loose bound of the thermodynamic uncertainty relation in a dissipative two-level quantum system
• Jensen bound for the entropy production rate in stochastic thermodynamics
• Bounds on skewness and kurtosis of steady state currents
• Understanding the level of Turbulence by Asymmetric Distributions: a motivation for measurements in Space Plasmas
• Thermodynamic bounds and symmetries in first-passage problems of fluctuating currents
• Inverse thermodynamic uncertainty relation and entropy production
• Thermodynamic uncertainty relation in the overdamped limit with a magnetic Lorentz force