Quantifying plasticity: a network-based framework linking structure to dynamical regimes

Abstract: Plasticity is a fundamental property of complex systems, such as the brain or an organism. Yet it typically remains a descriptive concept inferred retrospectively from observed outcomes, such as modifications in activity or morphology. Here, the network-based operationalization of plasticity is further formalized as the ratio between system size and connectivity strength among system elements. Within this framework, system size determines the dimensionality of the accessible state space, while connectivity strength tunes the system's regime. An optimal range of plasticity -- balancing capacity for change and capacity to maintain coherence -- emerges at intermediate connectivity strength. Notably, this balance coincides with the critical regime, which provides a theoretically motivated benchmark that enables a normalized unit of measure, termed effective plasticity, and comparisons of adaptive efficacy across diverse systems. Plasticity is thus transformed into a predictive tool that quantifies a system's capacity for change before it occurs. Its validity is supported across disciplines and, in particular, by evidence from psychopathology where it anticipates transitions between mental states. At a mechanistic level, plasticity acts as a structural tuning parameter for criticality, reframing their relationship as causal, with plasticity driving criticality rather than merely accompanying it. Furthermore, this network-based operationalization explains how larger systems can more robustly maintain critical dynamics. Crucially, the proposed perspective distinguishes functional regime shifts from thermodynamic phase changes, identifying plasticity as the system-level regulator that shapes and constrains the dynamic repertoire. This framework is applicable across domains, including ecology, economics, and social systems, and may foster cross-disciplinary integration within complexity science.