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Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Dec;88(6):062102. Epub 2013 Dec 2.

Work fluctuations in a time-dependent harmonic potential: rigorous results beyond the overdamped limit.

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  • 1Department of Physics, Myongji University, Yongin, Gyeonggi-Do 449-728, Korea.
  • 2Department of Physics, University of Seoul, Seoul 130-743, Republic of Korea and School of Physics, Korea Institute for Advanced Study, Seoul 130-722, Korea.
  • 3School of Physics, Korea Institute for Advanced Study, Seoul 130-722, Korea.


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 discussed in the overdamped limit.

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