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We study the dynamics of condensation of the inclusion process on aone-dimensional periodic lattice in the thermodynamic limit, generalisingrecent results on finite lattices for symmetric dynamics. Our main focus is ontotally asymmetric dynamics which have not been studied before, and which wealso compare to exact solutions for symmetric systems. We identify all relevantdynamical regimes and corresponding time scales as a function of the systemsize, including a coarsening regime where clusters move on the lattice andexchange particles, leading to a growing average cluster size. Suitableobservables exhibit a power law scaling in this regime before they saturate tostationarity following an exponential decay depending on the system size. Ourresults are based on heuristic derivations and exact computations for symmetricsystems, and are supported by detailed simulation data.

Dynamics of condensation in the totally asymmetric inclusion process