The historical Ornstein-Uhlenbeck process is defined by the Langevin equation for the velocity of a Brownian particle.
A multivariate Ornstein-Uhlenbeck process is a higher-dimensional extension of the latter.
It describes the coupled linear relaxational dynamics of several degrees of freedom subjected to additive noises.
Such a process is generically irreversible.
The corresponding nonequilibrium stationary state can be analyzed by means of linear algebra.
Its main characteristics, including probability current, entropy production rate, and fluctuation-dissipation ratio, can be expressed in terms of a single constant skew-symmetric matrix measuring the amount of irreversibility.
These concepts are illustrated by explicit results on arrays of resistively coupled RL and RC electrical circuits in an inhomogeneous temperature profile.

After arXiv:1807.00694