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

34 pages, 1 figure

References in corpus (3)

• Stationary and Nonequilibrium Fluctuations in Boundary Driven Exclusion Processes
• Symmetric inclusion process with slow boundary: hydrodynamics and hydrostatics
• Higher order hydrodynamics and equilibrium fluctuations of interacting particle systems

Cited by in corpus (3)

• Exact solution of an integrable non-equilibrium particle system
• Symmetric inclusion process with slow boundary: hydrodynamics and hydrostatics
• Duality in quantum transport models