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

TL;DR

This paper develops a large deviation theory for the entropy production rate of non-stationary stable Gauss-Markov chains, confirming the Gallavotti-Cohen symmetry and extending large deviation principles to quasi-Toeplitz quadratic functionals.

Contribution

It introduces a large deviation principle for entropy production in non-stationary stable Gauss-Markov chains, including boundary effects, and verifies the Gallavotti-Cohen symmetry.

Findings

Established a large deviation principle for entropy production rate.

Verified the Gallavotti-Cohen symmetry in this context.

Developed large deviation theory for quasi-Toeplitz quadratic functionals.

Abstract

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.