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Circuit topology of linear polymers: a statistical mechanical treatment

Circuit topology refers to the arrangement of interactions between objects belonging to a linearly ordered object set. Linearly ordered set of objects are common in nature and occur in a wide range of applications in economics, computer science, social science and chemical synthesis. Examples include linear bio-polymers, linear signaling pathways in cells as well as topological sorts appearing in project management. Using a statistical mechanical treatment, we study circuit topology landscapes of linear polymer chains with intra-chain contacts as a prototype of linearly sorted objects with interactions. We find generic features of the topological space and study the statistical properties of the space under the most basic constraints on the occupancy of arrangements and topological interactions. We observe that a set of correlated contact sites (a sector) could nontrivially influence the entropy of circuits as the number of involved sites increases. Finally, we discuss how constraints can be inferred from the information provided by local contact distributions in presence of a sector.