Work fluctuations in a time-dependent harmonic potential: rigorous results and beyond the overdamped limit
arXiv:1303.6742 · doi:10.1103/PhysRevE.88.062102
Abstract
We investigate the stochastic motion of a Brownian particle in the harmonic potential with a time-dependent force constant. It may describe the motion of a colloidal particle in an optical trap where the potential well is formed by a time-dependent field. We use the path integral formalism to solve the Langevin equation and the associated Fokker-Planck (Kramers) equation. Rigorous relations are derived to generate the probability density function for the time-dependent nonequilibrium work production beyond the overdamped limit. We find that the work distribution exhibits an exponential tail with a power-law prefactor, accompanied by an interesting oscillatory feature (multiple pseudo locking-unlocking transitions) due to the inertial effect. Some exactly solvable cases are also discussed in the overdamped limit.
12 pages, 7 figures
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