We consider the boundary driven harmonic model, which is exactly solvable, i.e., closed-form formulas for the multi-variate moments of the non-equilibrium steady state (NESS) can be produced (cf [1], [2]). Starting from this, we prove that the NESS is a mixture of equilibrium product measures, with parameters given by generalized order statistics. This form of NESS was conjectured in [4] for the KMP model, and proved with different methods for a special case in [5]. As a consequence, we prove the exact form of the large deviation rate function for the density profile. We also obtain an additivity principle for the pressure. In the talk, I will explain the context, starting from large deviations from the hydrodynamic limit and macroscopic fluctuation theory. Based on joint work with G. Carinci, C. Franceschini, R. Frassek, C. Giardina (Modena), see [6]. References [1] Frassek, Rouven, Cristian Giardina, and Jorge Kurchan. "Duality and hidden equilibrium in transport models." SciPost Physics 9.4 (2020): 054. [2] Frassek, Rouven, and Cristian Giardinà. "Exact solution of an integrable non-equilibrium particle system." Journal of Mathematical Physics 63.10 (2022). [3] Bertini, Lorenzo, Davide Gabrielli, and Joel L. Lebowitz. "Large deviations for a stochastic model of heat flow." Journal of statistical physics 121.5-6 (2005): 843-885. [4] Bertini, L., De Sole, A., Gabrielli, D., Jona-Lasinio, G., & Landim, C. (2007). Stochastic interacting particle systems out of equilibrium. Journal of Statistical Mechanics: Theory and Experiment, 2007(07), P07014. [5] Carinci, G., Franceschini, C., Gabrielli, D., Giardinà, C., & Tsagkarogiannis, D. (2023). Solvable stationary non equilibrium states. arXiv preprint arXiv:2307.02793. [6] Carinci, G., Franceschini, C., Frassek, R., Giardinà, C., & Redig, F. (2023). The open harmonic process: non-equilibrium steady state, pressure, density large deviation and additivity principle. arXiv preprint arXiv:2307.14975.