  The exchange-driven growth model describes a process in which pairs of
clusters interact through the exchange of single monomers. The rate of exchange
is given by an interaction kernel $K$ which depends on the size of the two
interacting clusters. Well-posedness of the model is established for kernels
growing at most linearly and arbitrary initial data.
  The longtime behavior is established under a detailed balance condition on
the kernel. The total mass density $\varrho$, determined by the initial data,
acts as an order parameter, in which the system shows a phase transition. There
is a critical value $\varrho_c\in (0,\infty]$ characterized by the rate kernel.
For $\varrho \leq \varrho_c$, there exists a unique equilibrium state
$\omega^\varrho$ and the solution converges strongly to $\omega^\varrho$. If
$\varrho > \varrho_c$ the solution converges only weakly to
$\omega^{\varrho_c}$. In particular, the excess $\varrho - \varrho_c$ gets lost
due to the formation of larger and larger clusters. In this regard, the model
behaves similarly to the Becker-D\"oring equation.
  The main ingredient for the longtime behavior is the free energy acting as
Lyapunov function for the evolution. It is also the driving functional for a
gradient flow structure of the system under the detailed balance condition.
