A simple information theoretic proof of the maximum entropy property of some Gaussian random fields.

A well known result of Burg (1967) and Kunsch (1981) identifies a Gaussian Markov random field with autocovariances specified on a finite part L of the n-dimensional integer lattice, as the random field with maximum entropy among all random fields with same autocovariance values on L. A simple information theoretic proof of a version of the maximum entropy theorem for random fields in n dimensions is presented in the special case that the given autocovariances are compatible with a unilateral autoregressive process.