A renewal approach to configurational entropy in one dimension

TL;DR

This paper presents a new renewal process-based method to calculate the configurational entropy of one-dimensional particle configurations, offering advantages over traditional transfer-matrix techniques.

Contribution

The paper introduces a systematic, easy-to-implement renewal approach for entropy calculation applicable to various local rules in 1D lattice models.

Findings

Applicable to models with local cluster rules

Simplifies entropy computation compared to transfer-matrix methods

Demonstrated on $k$-mer deposition and Rydberg atom ensembles

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 $b$.