Duality for Stochastic Models of Transport

We study three classes of continuous time Markov processes (inclusion process,
exclusion process, independent walkers) and a family of interacting diffusions (Brownian
energy process). For each model we define a boundary driven process which is obtained by
placing the system in contact with proper reservoirs, working at different particle densities
or different temperatures. We show that all the models are exactly solvable by duality, using
a dual process with absorbing boundaries. The solution does also apply to the so-called thermalization
limit in which particles or energy is instantaneously redistributed among sites.
The results shows that duality is a versatile tool for analyzing stochastic models of transport,
while the analysis in the literature has been so far limited to particular instances. Longrange
correlations naturally emerge as a result of the interaction of dual particles at the
microscopic level and the explicit computations of covariances match, in the scaling limit,
the predictions of the macroscopic fluctuation theory.