Large deviations and additivity principle for the open harmonic process

TL;DR

This paper rigorously derives macroscopic fluctuation properties for the open harmonic process, a model of energy transport with unbounded states, using explicit non-equilibrium steady state analysis.

Contribution

It provides the first rigorous derivation of large deviations and additivity principles for an energy transport model with unbounded state space.

Findings

Characterization of the stationary measure as a mixture of product measures

Identification of the mixture law in terms of the Dirichlet process

Verification of the fluctuation formulas predicted by Macroscopic Fluctuation Theory

Abstract

We consider the boundary driven harmonic model, i.e. the Markov process associated to the open integrable XXX chain with non-compact spins. Using the factorial moments we characterize the stationary measure as a mixture of product measures. For all spin values, we identify the law of the mixture in terms of the Dirichlet process. Next, by using the explicit knowledge of the non-equilibrium steady state we establish formulas predicted by Macroscopic Fluctuation Theory for several quantities of interest: the pressure (by Varadhan's lemma), the density large deviation function (by contraction principle), the additivity principle (by using the Markov property of the mixing law). To our knowledge, the results presented in this paper constitute the first rigorous derivation of these macroscopic properties for models of energy transport with unbounded state space, starting from the microscopic structure of the non-equilibrium steady state.