On a thermodynamically consistent modification of the Becker-Doering   equations
  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. 
Michael Herrmann, Margarita Naldzhieva, Barbara Niethammer