Effect of Landauer's blowtorch on the equilibration rate in a bistable potential

TL;DR

This paper investigates how localized heating (Landauer's blowtorch) affects the rate at which a particle in a double-well potential equilibrates, revealing that strategic placement of the hot zone can significantly enhance the process.

Contribution

It provides an analytical expression for the equilibration rate considering hot zone parameters and demonstrates the counterintuitive effect of hot zone placement on rate enhancement.

Findings

Hot zone increases equilibration rate.

Rate increases with hot zone strength and width.

Hot zone away from barrier top enhances rate more.

Abstract

Kinetic aspect of Landauer's blowtorch effect is investigated for a model double-well potential with localized heating. Using the supersymmetric approach, we derive an approximate analytical expression for the equilibration rate as function of the strength, width and the position of the hot zone, and the barrier height. We find that the presence of the hot zone enhances the equilibration rate, which is found to be an increasing function of the strength and width of the hot zone. Our calculations also reveal an intriguing result, namely, that placing the hot zone away from the top of the potential barrier enhances the rate more than when it is placed close to it. A physically plausible explanation for this is attempted. The above analytical results are borne out by detailed numerical solution of the associated Smoluchowski equation for the inhomogeneous medium.