On the relative stability of states and first-order phase transition in systems far from equilibrium

A method for classifying the states of a macroscopic dissipative system according to their stability with respect to finite-amplitude localized fluctuations and perturbations is presented. Since the method does not rely on a extremum principle it is applicable to open systems far from equilibrium. It appears that in general there exists at most one absolutely stable state (up to symmetry). Simple examples are given for systems without absolutely stable state.