Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium correlations

TL;DR

This paper extends classical dualities to boundary-driven particle systems with disorder, deriving new orthogonal polynomial dualities that reveal universal properties of non-equilibrium correlations.

Contribution

It introduces novel orthogonal polynomial dualities for disordered boundary-driven particle systems, generalizing classical dualities and establishing universal correlation properties.

Findings

Uniqueness of non-equilibrium steady states

Correlation inequalities in disordered systems

Universal properties of n-point correlations

Abstract

We consider symmetric partial exclusion and inclusion processes in a general graph in contact with reservoirs, where we allow both for edge disorder and well-chosen site disorder. We extend the classical dualities to this context and then we derive new orthogonal polynomial dualities. From the classical dualities, we derive the uniqueness of the non-equilibrium steady state and obtain correlation inequalities. Starting from the orthogonal polynomial dualities, we show universal properties of n-point correlation functions in the non-equilibrium steady state for systems with at most two different reservoir parameters, such as a chain with reservoirs at left and right ends.