Optimal potentials for temperature ratchets

TL;DR

This paper investigates the optimal potential profiles for temperature ratchets, revealing that certain idealized conditions can lead to divergent currents, which are mitigated in real-world scenarios.

Contribution

It derives the optimal potentials for temperature ratchets under various temperature profiles, highlighting the divergence in current for idealized piecewise constant temperature profiles.

Findings

Optimal potential maximizes current and power output.

Divergent current occurs in idealized temperature profiles.

Real experiments would observe finite currents due to physical limitations.

Abstract

In a spatially periodic temperature profile, directed transport of an overdamped Brownian particle can be induced along a periodic potential. With a load force applied to the particle, this setup can perform as a heat engine. For a given load, the optimal potential maximizes the current and thus the power output of the heat engine. We calculate the optimal potential for different temperature profiles and show that in the limit of a periodic piecewise constant temperature profile alternating between two temperatures, the optimal potential leads to a divergent current. This divergence, being an effect of both the overdamped limit and the infinite temperature gradient at the interface, would be cut off in any real experiment.