bibkey: “schnakenberg1976network” authors: “J. Schnakenberg” year: 1976 title: “Network theory of microscopic and macroscopic behavior of master equation systems” doi: “10.1103/RevModPhys.48.571” url: “https://doi.org/10.1103/RevModPhys.48.571” claim: “A finite master-equation network admits a cycle-and-affinity description, with stationary currents constrained by Kirchhoff conservation.” strata_touched: [] license: “citation-only” triage: “anchor”

Network theory of microscopic and macroscopic behavior of master equation systems

Reviews of Modern Physics 48, 571–585 (1976). Section VIII, pages 580–582, develops cycles and affinities; section IX, page 583, expresses stationary current conservation and macroscopic entropy production in this framework.

This is literature-attested background for decomposing currents and edge affinities. The finite discrete-time parity-kernel proof computes its own transition ratios and endpoint corrections; this citation supplies neither the optimized information-threshold asymptotic nor the trajectory-testing Poisson limit. No general cycle-decomposition theorem is claimed as new.

Primary text: https://harvest.aps.org/v2/journals/articles/10.1103/RevModPhys.48.571/fulltext.