Bio-homeostasis Information Theory: A Resource Audit Framework for Statistical Pattern Maintenance in Dynamical Systems

Living systems and life-like dynamical systems undergo significant changes in their states and structures when subjected to interventions such as treatment, stimulation, training, or recovery. Despite different mechanisms across fields (ranging from cellular perturbation systems, cancer therapy, neurodegenerative interventions, neural interfaces, cognitive-behavioral interventions, to persistent artificial intelligence agents), they share a common structural problem: when bifurcations accumulate gradually, precisely how much resource is required to maintain a declared statistical pattern of the system within an acceptable neighborhood? To address this question, we propose Bio-homeostasis Information Theory (BIT), constructed as a statistical homeostasis auditing framework. In this framework, “Bio-homeostasis” denotes the resource-constrained maintenance, restoration, transfer, or reconstruction of statistical patterns under changing conditions. BIT defines system class, measurement family, feature library, bifurcation process, innovation source, distortion function, budget constraint, and bridging residual. Its core demand metric is the bifurcation information rate, derived from the converse of rate-distortion theory: if the effective correction budget falls below the rate required to keep innovation distortion within the declared tolerance, then it is impossible to maintain the declared statistical pattern of the system within an acceptable neighborhood. The central contributions of this work are: (1) unifying multiple mechanistically disparate domains into a resource-constrained statistical pattern maintenance problem; (2) introducing the bifurcation information rate as a quantitatively computable necessary condition; (3) proposing the demand–budget–bridge triad, which distinguishes BIT from classical homeostasis, control theory, and active inference; and (4) systematically defining failure modes (budget insufficiency, feature library mismatch, noisy budget measurement, and bridging failure) and providing experimental requirements and synthetic demonstrations. Collectively, BIT provides a new theoretical foundation for resource management in dynamical systems across the life sciences and artificial intelligence.