A renewal approach to configurational entropy in one dimension

Abstract

We introduce a novel approach, inspired from the theory of renewal processes, to determine the configurational entropy of ensembles of constrained configurations of particles on the one-dimensional lattice. The proposed method can deal with all local rules involving only the lengths of clusters of occupied and empty sites. Within this scope, this method is both more systematic and easier to implement than the transfer-matrix approach. It is illustrated in detail on the $k$-mer deposition model and on ensembles of trapped Rydberg atoms with blockade range $b$.

29 pages, 8 figures, 1 table

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Cited by in corpus (3)

• Jamming and metastability in one dimension: from the kinetically constrained Ising chain to the Riviera model
• On the structure factor of jammed particle configurations on the one-dimensional lattice
• Random sequential covering of a one-dimensional lattice by $k$-mers