Duality for a boundary driven asymmetric model of energy transport

TL;DR

This paper introduces a duality relation between a boundary-driven asymmetric energy transport model and a symmetric process, enabling analytical computation of stationary measure moments.

Contribution

It establishes a novel duality between an asymmetric energy model and a symmetric inclusion process with boundary conditions, using a non-local transformation.

Findings

Duality relation allows analytical calculation of exponential moments.

Model is shown to be dual to the symmetric inclusion process.

The approach provides insights into energy transport with boundary effects.

Abstract

We study the Asymmetric Brownian Energy, a model of heat conduction defined on the one-dimensional finite lattice with open boundaries. The system is shown to be dual to the Symmetric inclusion process with absorbing boundaries. The proof relies on a non-local map transformation procedure relating the model to its symmetric version. As an application, we show how the duality relation can be used to analytically compute suitable exponential moments with respect to the stationary measure.