Large Deviations and Additivity Principle for the Open Harmonic Process
G Carinci (TU Delft - Applied Probability, Università Degli Studi di Modena e Reggio Emilia)
Chiara Franceschini (Università Degli Studi di Modena e Reggio Emilia)
Rouven Frassek (Università Degli Studi di Modena e Reggio Emilia)
C. Giardinà (TU Delft - Applied Probability, Università Degli Studi di Modena e Reggio Emilia)
FHJ REDIG (TU Delft - Applied Probability)
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Abstract
We consider the boundary driven harmonic model, i.e. the Markov process associated to the open integrable XXX chain with non-compact spins. We characterize its 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.
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