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Charged particle in a magnetic field: Jarzynski equality
1Institute of Physics, Bhubaneswar 751005, India. jayan@iopb.res.in
Summary
This study demonstrates solvable models illustrating the Jarzynski theorem and fluctuation theorems for a charged particle in a magnetic field. The findings complement classical theorems regarding diamagnetism in equilibrium systems.
Area of Science:
- Statistical Mechanics
- Quantum Mechanics
- Condensed Matter Physics
Background:
- The Jarzynski theorem relates non-equilibrium work to equilibrium free energy.
- Fluctuation theorems provide insights into the statistical behavior of systems driven far from equilibrium.
- The Bohr-van Leeuwen theorem states that classical magnetic susceptibility is zero.
Purpose of the Study:
- To illustrate the Jarzynski theorem and related fluctuation theorems using solvable models.
- To investigate the behavior of a charged particle in a magnetic field within a harmonic potential.
- To explore the relationship between non-equilibrium dynamics and equilibrium properties.
Main Methods:
- Development of solvable models for a charged particle in a 2D harmonic potential subjected to a magnetic field.
- Analysis of two scenarios: translation of the harmonic potential center and application of an AC force.
- Application of the Jarzynski identity and comparison with the Bohr-van Leeuwen theorem.
Main Results:
- Demonstration of solvable models that exemplify the Jarzynski theorem and fluctuation theorems.
- The Jarzynski identity is shown to complement the Bohr-van Leeuwen theorem.
- Insights into the behavior of diamagnetism in classical equilibrium systems are provided.
Conclusions:
- Solvable models can effectively illustrate fundamental theorems in non-equilibrium statistical mechanics.
- The Jarzynski theorem offers a bridge between non-equilibrium work and equilibrium thermodynamics.
- The study highlights the interplay between classical equilibrium properties and non-equilibrium dynamics.
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