Overdamped Brownian dynamics in a potential trap under a nonuniform temperature field

Abstract

We investigate the dynamics and statistics of a one-dimensional Brownian particle in a potential trap under a spatially nonuniform temperature field. For single minimum harmonic or anharmonic trapping potentials and unimodal temperature field, the Brownian particle can be described by a double-well effective potential with an effective barrier, with the effective potential and the steady-state position distribution derived analytically using the Fokker-Planck equation. The transition rate between the two wells in the effective potential is also derived. In addition, the impact of a nonuniform temperature on the escape kinetics in a double-well potential is also considered with the modified transition rate derived analytically, indicating suppression of the energy barrier and hence enhancement of the transition rate between the two wells. Furthermore, it is demonstrated that a tilted double-well effective potential can be obtained by mismatching the centers of the trapping well and the temperature profile, opening the possibility of constructing a memory erasure device in such a system. The nonequilibrium nature due to the temperature gradient is also discussed in terms of the hidden entropy production, as revealed by the corresponding underdamped dynamics. Numerical simulations of the corresponding Langevin dynamics verify all of these theoretical results.