A study of inertial effects on the efficiency and transport coherence of a shifting Brownian Motor

We investigate the role of inertia on the performance of a shifting Brownian motor through extensive numerical simulations of the Langevin equation. The motor consists of a Brownian particle subjected alternately to two spatially asymmetric and piecewise-linear potentials whose extrema are shifted relative to each other. Our results reveal several distinctive features absent in previous overdamped models. In the deterministic, overdamped, and adiabatic regime, the motor exhibits giant transport coherence (Peclet number (Pe>105) with negligible dispersion and maximum efficiency (∼8%). Transport coherence degrades monotonically with increasing particle mass, temperature, and in the non-adiabatic limit. At higher temperatures, we identify an optimal mass (∼M=1) maximizing both work output and thermodynamic efficiency, reflecting a balance between thermal activation and inertial momentum. A counterintuitive, non-monotonic temperature dependence of the effective diffusion coefficient emerges at large masses, which we explain through coexisting locked and running states of motion. Our analytical predictions for current, efficiency, and energy input in the overdamped-deterministic-adiabatic limit show excellent agreement with numerical results. These findings provide design principles for optimizing nanoscale motors and offer insights into the complex interplay between deterministic forces, thermal fluctuations, and inertial dynamics in non-equilibrium transport.