Dynamic phase transitions in nonequilibrium processes

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Abstract
Unstable, time-independent transitions that cause changes in the spatial symmetry of a nonequilibrium system are analyzed. The physiochemical processes include the nucleation, growth, and dissociation of particle aggregates and molecular diffusion. A bifurcation problem is treated in which there occurs a time-independent transition to a spatially inhomogeneous stationary solution of the nonlinear diffusion equation. Repeated instability and branching can occur through the excitation and interaction of the harmonics that the perturbation comprises. New stationary regimes, each with a different spatial symmetry, can be attained by the superposition of a stable stationary value of the perturbation upon the unstable stationary solution. Harmonic interactions cause stationary-state branching and shifting. Asymptotically, the nonequilibrium system approaches a stable, time-independent spatial configuration that is an inherent property of the system itself. Instabilities occur in the direction of stationary regimes with decreasing characteristic dimensions and are shown to increase the number of degrees of freedom of the system. The transitions are (i) considered to be the zero-frequency analog of the transition between laminar and turbulent flow proposed by Landau and (ii) resemble thermodynamically a second-order phase transition. The second variation of the entropy contained in the first harmonic of the perturbation vanishes at the critical point. Energy-transfer mechanisms of unstable transitions are discussed.

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