Irreversible processes at nonequilibrium steady states

It is shown that a Liapunov criterion exists for the stability of nonequilibrium steady states. This criterion is based upon the fluctuation-dissipation relation, as was first pointed out by Keizer. At steady states, the Liapunov function is constructed from the covariance matrix for the thermodynamic variables. Unlike the situation around equilibrium, at steady states the covariance matrix and the "excess entropy" matrix are not equivalent. The excess entropy, which serves as the Liapunov function around equilibrium, does not work in this capacity at steady states. Keizer's Liapunov function must be viewed as the first correct candidate for a proper Liapunov function for steady states.