Asymptotics of work distribution for a Brownian particle in a time-dependent anharmonic potential

Abstract

The work distribution of a driven Brownian particle in an anharmonic potential is studied. The potential consists of two components: a harmonic part with a time-dependent stiffness and a time-independent logarithmic part. For arbitrary driving of the stiffness, the problem of solving the evolution equation for the joint probability density of work and particle position reduces to the solution of a Riccati differential equation. For a particular driving protocol, the Riccati equation can be solved and the exact large-work representation of the work distribution can be calculated. We propose a general form of the tail behavior. The asymptotic analysis of the work distribution is of vital importance for obtaining equilibrium free energy differences in experiments based on the Jarzynski identity. In the absence of the logarithmic component, our results agree with the work distribution for driven Brownian motion in a harmonic potential.