  This article explores the application of the path integral formalism in
describing synchronization phenomena in entangled networks, cavities, and
reservoirs. We discuss the concept of using Lagrangian mechanics for systems
undergoing synchronization and its connection to least-action principles. By
replacing the concept of least action with a least signaling term, we
investigate how the path integral representation can be applied to study
synchronization dynamics in entangled networks, drawing parallels with coupled
oscillators in phase space models such as the Kuramoto model, as well as its
relation to algorithms, such as the firefly algorithm for potential use in
optimization in networks. This article also illustrates how entanglement
signals themselves can interact strongly with ordered systems of harmonic
oscillators that reach thresholds of classical synchronization with potential
therefore for using entangled signals as weak measurement probes where phase
dynamics is of interest.
