On Complexity in Resource Constrained Neuronal Systems: Dynamic Resource Theory

Understanding how complex systems self-organize, exhibit emergent properties beyond their constituent elements remains a challenge across physics, biology, and cognitive science. In resource-constrained neuronal systems, existing theoretical approaches, including gauge theoretic formulations, statistical physics-inspired methods, dynamical population models, and variational principles such as the Free Energy Principle, address important aspects of this problem but do not fully specify the physical conditions and thermodynamic costs under which self-organizing behavior occurs. Here, we introduce Dynamic Resource Theory (DRT) as a general physical framework for describing self-organization under constrained resource availability. DRT formalizes complexity as a physical property of self-organizing systems arising from coupled mechanisms of resource allocation and dynamic reallocation of internal resources. This framework provides a thermodynamic and variational account of how stability is preserved while adaptive reconfiguration remains possible, consistent with stationary action and thermodynamic constraints. DRT is formulated within a gauge theoretic setting and directly incorporates the energetic costs associated with maintaining structure and enabling system-level reconfiguration. Within DRT, baseline resource allocation preserves system stability, while internal and external demands perturb the system, driving self-organization through dynamic resource reallocation across a coupled free energy landscape without assuming subsystem separability. We then develop Neural Resource Theory (NRT) and Cognitive Resource Theory (CRT) as principled specializations of DRT, illustrating how this structure is instantiated in resource constrained neuronal and cognitive systems. We conclude by discussing the broader implications of DRT for understanding how complexity, emergence, and adaptive capacity arise over time through thermodynamically permissible reallocation processes across scales.