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Keywords:

  • Dynamics of first-order phase transitions;
  • Generalized nucleation theories;
  • Nonequilibrium thermodynamics;
  • Infinite systems of ordinary differential equations

Abstract

The infinite set of cluster equations, proposed by Binder and Müller-Krumbhaar for a Glauber kinetic Ising ferromagnet in 1974, generalize the Becker-Döring equations used in classical nucleation theory. For positive symmetric transition rates satisfying certain growth conditions and a detailed balance condition we prove for sufficiently fast decaying initial cluster distributions the existence of a positive cluster distribution with finite density for all finite times solving the cluster equations. Uniqueness is proven under some further conditions on the transition rates. Our existence and uniqueness results apply e.g. for a Glauber kinetic Ising ferromagnet in two dimensions.