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Fluctuation theorems for systems under Fokker-Planck dynamics.
A Pérez-Madrid1, I Santamaría-Holek
1Departament de Física Fonamental, Facultat de Física, Universitat de Barcelona, Avenida Diagonal 647, 08028 Barcelona, Spain.
Summary
This study explores Brownian motion under conservative and nonconservative forces. We derived the Fokker-Planck equation and fluctuation theorem expressions using a thermodynamic approach.
Area of Science:
- Thermodynamics
- Statistical Mechanics
- Nonlinear Dynamics
Background:
- Brownian motion is a fundamental concept in statistical physics.
- Understanding particle dynamics under external forces is crucial.
- Existing theories often focus on specific types of forces.
Purpose of the Study:
- To investigate Brownian motion driven by both conservative and nonconservative forces.
- To derive the Fokker-Planck equation for this system.
- To obtain expressions for the fluctuation theorem under different equilibrium conditions.
Main Methods:
- Thermodynamic approach to Brownian motion theory.
- Derivation of the Fokker-Planck equation.
- Analysis of fluctuation theorem in local and quasiequilibrium.
Main Results:
- Successfully obtained the Fokker-Planck equation for the studied system.
- Derived expressions for the fluctuation theorem in local and quasiequilibrium.
- Confirmed that results in local equilibrium match previous findings.
Conclusions:
- The thermodynamic approach provides a unified framework for studying Brownian motion.
- The derived fluctuation theorem expressions are valid for both equilibrium conditions.
- This work advances the understanding of non-equilibrium statistical mechanics.
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