Heat Out of Equilibrium Driven by Potential Pulling Beyond the Overdamped Limit

Abstract

We investigate heat accumulated for a long period time in nonequilibrium motion of a colloid under a potential with center pulled by a constant velocity. Heat and work have the same average value in steady state, but the distribution functions for thermal fluctuations are different. Difference comes from everlasting memory of initial high energy on total amount of accumulated heat. As a result, the positive tail of the heat distribution exhibits a distinct correction to the large deviation function, compared to a usual logarithmic correction. Mathematically, difference originates from the singularity in the generating function, the Fourier transform, of the distribution function and makes usual saddle point approximation not valid. We use the modified saddle point approximation technique to compute the heat distribution function. We find the heat distribution for the underdamped case and find the correction to large deviation function more predominant than for the overdamped case.