Large deviations for quadratic functionals of stable Gauss–Markov chains and entropy production

In this paper, we establish a large deviation principle for the entropy production rate of possible non-stationary, centered stable Gauss–Markov chains, verifying the Gallavotti–Cohen symmetry. We reach this goal by developing a large deviation theory for quasi-Toeplitz quadratic functionals of multivariate centered stable Gauss–Markov chains, which differ from a perfect Toeplitz form by the addition of quadratic boundary terms.