ORDER-WINDOW DYNAMICS

Order-Window Dynamics (OWD) is a carrier-based framework for analysing the formation, persistence, transition, and failure of observable states in open dissipative systems. OWD does not replace established physical theories or governing equations. Instead, it provides a structured interface for translating the outputs of domain-specific models into explicit and testable viability conditions. Core Idea Physical systems often remain operational only within bounded regions. More energy, stronger coupling, greater dissipation, or a larger sink capacity are not necessarily beneficial without limit. Their effect depends on location, direction, accessibility, system state, timing, and interaction with other necessary functions. OWD therefore treats viability as the simultaneous satisfaction of several predeclared functional margins. The function closest to its boundary is identified as the currently limiting mechanism. Framework Architecture OWD distinguishes three analytical levels: Dynamical carrierThe established domain-specific model that generates physically accessible system trajectories. Thermodynamic admissibilityCompliance with conservation laws, constitutive restrictions, irreversible transport, and the entropy inequality. Viability analysisEvaluation of whether a predefined observable state can form, persist, transition, or fail within a declared spatial and temporal window. The framework requires spatially resolved variables, directed coupling pathways, bounded operating regions, characteristic time scales, history dependence where physically justified, and explicit measurement and model uncertainty. Scientific Contribution OWD addresses a recurring problem in multiphysics analysis: established models can describe individual physical processes accurately while leaving the combined functional conditions of system viability implicit. The framework provides a common procedure for making these conditions explicit without erasing the differences between physical disciplines. Its purpose is not to create a universal physical equation, but to establish a reproducible and falsifiable translation layer between specialised models and observable operational outcomes. Development Evidence The architecture was refined through retrospective stress tests involving: tropical cyclones, magnetically confined fusion-plasma exhaust, transitional pipe flow, critical heat flux, hypersonic scramjet combustion. These cases rejected simpler formulations based on global input, global dissipation, static interface conditions, monotonic benefit assumptions, or instantaneous state alone. The surviving framework requires zonal analysis, directed transfer, finite accessibility, upper and lower operating limits, temporal pathways, and explicit uncertainty. Evidential Status The completed cases form a development set. They demonstrate physical compatibility, operational feasibility, and the ability of OWD to expose inadequate model forms. They do not yet establish OWD as an independently validated predictive theory. Prospective confirmation must test a frozen framework against established domain controls and the strongest appropriate baseline models. OWD must be rejected or restricted to diagnostic use if its variables cannot be independently operationalised, if it adds no reproducible information beyond existing models, or if its results require post-outcome redefinition. Practical Relevance Potential applications include: identification of limiting subsystems, description of safe and viable operating windows, early warning of transitions and failure, comparison of reduced and high-fidelity models, detection of missing measurements or coupling pathways, transparent communication of uncertainty, design of prospective experiments and monitoring systems. Relation to the Working Paper The publication is a substantially revised and consolidated development of the preceding Order-Window Dynamics Working Paper. The earlier working paper documents the conceptual and methodological development of the framework. The present publication formalises its architecture, evidential boundaries, falsification criteria, and planned validation pathway.