Distribution of work in isothermal nonequilibrium processes

Diffusive motion in an externally driven potential is considered. It is shown that the distribution of work required to drive the system from an initial equilibrium state to another is Gaussian for slow but finite driving. Our result is obtained by projection method techniques exploiting a small parameter defined as the switching rate between the two states of the system. The exact solution for a simple model system shows that such an expansion may fail in higher orders, since the mean and the variance following from the exact distribution show nonanalytic behavior.

Figure 1

Scheme of the experiment of Ref. 1. A colloidal particle at position $x\left(t\right)$ is dragged by an optical tweezer with focus at $y\left(\mathrm{\lambda }\right)=L\mathrm{\lambda }$ through a viscous fluid. The effective potential is harmonic with a spring constant $k$.