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Work fluctuations in a time-dependent harmonic potential: rigorous results beyond the overdamped limit
Chulan Kwon1, Jae Dong Noh2, Hyunggyu Park3
1Department of Physics, Myongji University, Yongin, Gyeonggi-Do 449-728, Korea.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 4, 2014
Summary
We studied Brownian particle motion in a time-dependent optical trap. Inertial effects cause oscillatory features in work distribution, going beyond simple models.
Area of Science:
- Statistical Mechanics
- Soft Matter Physics
- Non-equilibrium Thermodynamics
Background:
- Brownian motion describes particle movement due to random collisions.
- Optical traps use light to confine particles, relevant for colloidal systems.
- Time-dependent potentials are crucial for understanding dynamic systems.
Purpose of the Study:
- Investigate stochastic motion of Brownian particles in time-dependent harmonic potentials.
- Analyze non-equilibrium work production beyond the overdamped limit.
- Explore the impact of inertial effects on work distribution.
Main Methods:
- Path integral formalism to solve Langevin and Fokker-Planck (Kramers) equations.
- Derivation of rigorous relations for probability density function.
- Analysis of systems beyond the overdamped limit.
Main Results:
- Work distribution shows an exponential tail with a power-law prefactor.
- Inertial effects lead to oscillatory features (pseudo-locking-unlocking transitions).
- Exact solutions are discussed for the overdamped limit.
Conclusions:
- The study provides a rigorous framework for non-equilibrium work in dynamic systems.
- Inertial effects significantly alter work distribution, revealing complex dynamics.
- Findings are relevant for colloidal dynamics in time-varying optical traps.
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