Theory of nonequilibrium first-order phase transitions for stochastic dynamics

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Abstract
A dynamic definition of a first-order phase transition is given. It is based on a master equation description of the time evolution of a system. When the operator generating that time evolution has an isolated near degeneracy there is a first-order phase transition. Conversely, when phenomena describable as first-order phase transitions occur in a system, the corresponding operator has near degeneracy. Estimates relating degree of degeneracy and degree of phase separation are given. This approach harks back to early ideas on phase transitions and degeneracy, but now enjoys greater generality because it involves an operator present in a wide variety of systems. Our definition is applicable to what have intuitively been considered phase transitions in nonequilibrium systems and to problematic near equilibrium cases, such as metastability.