The "harmonic liquid" away from equilibrium. I. Stationary correlation functions

Some aspects of the linear chain of harmonic oscillators ("harmonic liquid") are studied. In particular we compute the stationary correlation functions of coordinates and momenta of the oscillators for a particular non-equilibrium steady state. We find that the coordinates and momenta autocorrelation functions are analogous to their equilibrium counterparts whereas the coordinates-momenta correlation functions exhibit long-range behaviour due to time reversal symmetry breaking. The non-equilibrium entropy of the chain is also computed. It contains a non-equilibrium part that depends on the temperature of the external sources and on the stationary temperature. A comparison with a non-equilibrium entropy obtained from information theory is made. © 1988.