Petrov-Galerkin model reduction for thermochemical nonequilibrium gas mixtures: Application to the N₂+N system

State-specific thermochemical collisional models are essential for accurately describing the physics of systems with nonequilibrium plasmas. However, these models are computationally expensive and impractical for large-scale, multi-dimensional simulations. To address this, the complexity of the governing equations has traditionally been reduced using empirical or physics-based approaches, but these often lead to inaccuracies and fail to capture key features of the original physics. In this paper, we apply a recently proposed model reduction pipeline to the N₂+N system, which is based on the Petrov-Galerkin projection of nonlinear kinetic equations onto a low-dimensional subspace. This approach is motivated by the observation that this kinetic system typically exhibits low-rank dynamics, driving the state towards a low-dimensional subspace suitable for reduced-order modeling. Despite the nonlinear nature of the governing equations, we take advantage of the linearized equations around thermochemical equilibrium steady states to identify the subspaces on which the system evolves, reducing the cost associated with the identification of the reduced-order model. The method achieves high accuracy, with relative errors under 1% for macroscopic quantities (e.g., moments) and around 10% for microscopic quantities (e.g., energy level populations), while also delivering excellent compression rates and speedups.