On a thermodynamically consistent modification of the Becker-Doering equations

TL;DR

This paper analyzes a thermodynamically consistent modification of the Becker-Doering equations, establishing mathematical properties, equilibrium conditions, and long-term behavior of the modified system.

Contribution

It provides existence, uniqueness, and equilibrium criteria for the modified Becker-Doering equations with a nonconvex Lyapunov function.

Findings

Existence and uniqueness of solutions established.

Explicit criterion for equilibrium states derived.

Long-term behavior analyzed under equilibrium conditions.

Abstract

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.