Duality relations in single-file diffusion

TL;DR

This paper establishes a general duality relation in single-file diffusion systems within fluctuating hydrodynamics, enabling the mapping of any such system onto a dual system to derive new results from known solutions.

Contribution

It introduces a universal duality relation for single-file diffusion models within hydrodynamics, broadening the scope beyond specific microscopic models.

Findings

Duality relations are not model-specific and hold generally in the hydrodynamic limit.

Any single-file system can be mapped onto a dual system within the hydrodynamic framework.

This duality enables deriving new results from existing solutions of dual models.

Abstract

Single-file transport, which corresponds to the diffusion of particles that cannot overtake each other in narrow channels, is an important topic in out-of-equilibrium statistical physics. Various microscopic models of single-file systems have been considered, such as the simple exclusion process, which has reached the status of a paradigmatic model. Several different models of single-file diffusion have been shown to be related by a duality relation, which holds either microscopically or only in the hydrodynamic limit of large time and large distances. Here, we show that, within the framework of fluctuating hydrodynamics, these relations are not specific to these models and that, in the hydrodynamic limit, every single-file system can be mapped onto a dual single-file system, which we characterise. This general duality relation allows us to obtain new results for different models, by exploiting the solutions that are available for their dual model.