Langevin approach to the Porto system

TL;DR

This paper extends Porto's molecular motor model by incorporating stochastic forces and Langevin dynamics, confirming unidirectional rotor motion at finite temperatures and energy accumulation in a potential field.

Contribution

It generalizes Porto's deterministic system to include thermal effects using Langevin equations, revealing new mechanisms for unidirectional motion and energy storage.

Findings

Unidirectional rotor motion confirmed at nonzero temperatures.

Motion persists in the presence of a weak potential field.

Rotor can accumulate potential energy from thermal bath.

Abstract

M. Porto (Phys. Rev. E 63 (2001) 030102) suggested a system consisting of Coulomb interacting particles, forming a linear track and a rotor, and working as a molecular motor. Newton equations with damping for the rotor coordinate on the track x, with a prescribed time-dependence of the rotor angle theta, indicated unidirectional motion of the rotor. Here, for the same system, the treatment was generalized to nonzero temperatures by including stochastic forces and treating both x and theta via two coupled Langevin equations. Numerical results are reported for stochastic homogeneous distributions of impact events and Gaussian distributions of stochastic forces acting on both the variables. For specific values of parameters involved, the unidirectional motion of the rotor along the track is confirmed, but with a mechanism that is not necessarily the same as that one by Porto. In an additional weak homogeneous potential field U(x)=const.x acting against the motion, the unidirectional motion persists. Then the rotor accumulates potential energy at the cost of thermal stochastic forces from the bath.