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Recently, Dreyer and Duderstadt have proposed a modification of the
Becker-Doering cluster equations which now have a nonconvex
Lyapunov function. We start with existence and uniqueness results
for the modified equations. Next we derive an explicit criterion for
the existence of equilibrium states and solve the minimization
problem for the Lyapunov function. Finally, we discuss the long time
behavior in the case that equilibrium solutions do exist.