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We prove that time dynamics of a stochastic process of pure coagulation isgiven by a time dependent Gibbs distribution if and only if rates of singlecoagulations have the form $\psi(i,j)=if(j)+jf(i)$, where $f$ is an arbitrarynonnegative function on the set of integers $\ge 1$. We also obtained arecurrence relation for weights of these Gibbs distributions, that allowedexplicit solutions in three particular cases of the function $f$. For the threecorresponding models, we study the probability of coagulation into one giantcluster, at time $t>0.$

Coagulation processes with Gibbsian time evolution