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Related Concept Videos

Magnetic Fields01:27

Magnetic Fields

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A moving charge or a current creates a magnetic field in the surrounding space, in addition to its electric field. The magnetic field exerts a force on any other moving charge or current that is present in the field. Like an electric field, the magnetic field is also a vector field. At any position, the direction of the magnetic field is defined as the direction in which the north pole of a compass needle points.
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An electric field suffers a discontinuity at a surface charge. Similarly, a magnetic field is discontinuous at a surface current. The perpendicular component of a magnetic field is continuous across the interface of two magnetic mediums. In contrast, its parallel component, perpendicular to the current, is discontinuous by the amount equal to the product of the vacuum permeability and the surface current. Like the scalar potential in electrostatics, the vector potential is also continuous...
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Magnetic Field due to Moving Charges01:23

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A stationary charge creates and interacts with the electric field, while a moving charge creates a magnetic field.
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Magnetic Field Of A Current Loop01:16

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Consider a circular loop with a radius a, that carries a current I. The magnetic field due to the current at an arbitrary point P along the axis of the loop can be calculated using the Biot-Savart law.
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Consider a plane wavefront traveling in position x-direction with a constant speed. This wavefront can be utilized to obtain the relationship between electric and magnetic fields with the help of Faraday's law.
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Fluctuation relations for systems in a constant magnetic field.

Alessandro Coretti1, Lamberto Rondoni2, Sara Bonella3

  • 1Department of Mathematical Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy and Centre Européen de Calcul Atomique et Moléculaire (CECAM), École Polytechnique Fédérale de Lausanne, Batochime, Avenue Forel 2, 1015 Lausanne, Switzerland.

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Summary

This study validates fluctuation relations (FRs) for magnetic field systems without field inversion. New time-reversal symmetries prove transient FRs and derive steady-state FRs, enhancing statistical mechanics predictions.

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Area of Science:

  • Statistical Mechanics
  • Nonlinear Dynamics
  • Condensed Matter Physics

Background:

  • Fluctuation relations (FRs) are crucial in statistical mechanics, but their validity in systems with magnetic fields is complex.
  • Traditional proofs often require magnetic field inversion, limiting applicability.
  • Deterministic thermostats and time-reversal symmetries offer new avenues for theoretical analysis.

Purpose of the Study:

  • To investigate the validity of fluctuation relations (FRs) in systems subjected to a constant magnetic field.
  • To prove transient FRs without relying on magnetic field inversion.
  • To derive steady-state FRs under specific conditions and extend the predictive power of statistical mechanics.

Main Methods:

  • Utilized recently introduced time-reversal symmetries applicable to static electric and magnetic fields.
  • Employed deterministic thermostats to establish theoretical frameworks.
  • Derived transient and steady-state fluctuation relations analytically.

Main Results:

  • Successfully proved transient fluctuation relations (FRs) without invoking magnetic field inversion.
  • Derived steady-state FRs under the t-mixing condition.
  • Demonstrated extended predictive power through analysis of nonlinear response and dissipation cumulants.

Conclusions:

  • The study confirms the validity of fluctuation relations in constant magnetic fields using novel symmetry approaches.
  • The derived FRs offer analytical methods for determining null cumulants in systems with magnetic fields.
  • These findings significantly advance the application and understanding of statistical mechanics in complex systems.