We investigate the rate of convergence to equilibrium for subcritical solutions to the
Becker–Döring equations with physically relevant coagulation and fragmentation
coefficients and mild assumptions on the given initial data. Using a discrete version of
the log-Sobolev inequality with weights, we show that in the case where the
coagulation coefficient grows linearly and the detailed balance coefficients are of
typical form, one can obtain a linear functional inequality for the dissipation of the
relative free energy. This results in showing Cercignani’s conjecture for the
Becker–Döring equations and consequently in an exponential rate of convergence to
equilibrium. We also show that for all other typical cases, one can obtain an “almost”
Cercignani’s conjecture, which results in an algebraic rate of convergence to
equilibrium.