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Fluctuation relations for a classical harmonic oscillator in an electromagnetic field.
J I Jiménez-Aquino1, R M Velasco, F J Uribe
1Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, Apartado Postal 55-534, C.P. 09340, México, Distrito Federal, Mexico. ines@xanum.uam.mx
Summary
This study explores fluctuation relations in classical charged harmonic oscillators under electromagnetic fields. It quantifies irreversible behavior and verifies key theorems like Jarzynski equality under driven, non-equilibrium conditions.
Area of Science:
- Statistical Mechanics
- Electromagnetism
- Non-equilibrium Thermodynamics
Background:
- Classical systems driven away from equilibrium exhibit unique thermodynamic behaviors.
- Fluctuation relations provide insights into irreversibility in physical processes.
- Electromagnetic fields significantly influence the dynamics of charged particles.
Purpose of the Study:
- To establish fluctuation relations for a 2D system of charged harmonic oscillators in an electromagnetic field.
- To quantify irreversible behavior using trajectory probabilities and work done.
- To verify the work-fluctuation theorem and Jarzynski equality.
Main Methods:
- Theoretical analysis of classical two-dimensional systems.
- Derivation of fluctuation relations based on work performed by electric fields.
- Comparison with existing results for noninteracting electrons in crossed fields.
Main Results:
- Established fluctuation relations for charged harmonic oscillators under electromagnetic fields.
- Demonstrated that results reduce to known relations for noninteracting electrons in specific limits.
- Verified the work-fluctuation theorem and Jarzynski equality by considering harmonic trap potential dynamics.
Conclusions:
- The study provides a theoretical framework for understanding non-equilibrium thermodynamics in driven harmonic oscillator systems.
- The findings bridge the gap between simple noninteracting systems and more complex harmonic oscillator models.
- The work-fluctuation theorem and Jarzynski equality hold for these classical driven systems.
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