Hamiltonian Dynamics as the Engine of Biological Computation: Linking Gamma Oscillations to Scale-Inseparable Memory

This study investigates the physical basis of biological computation, focusing on the tension between static structuralism and dynamic evolution. Utilizing a Hamiltonian formulation of the Kuramoto model, we simulate a biological reservoir to rigorously evaluate the relationship between “Scale Inseparability” (coupling strength), Gamma oscillations (30-50 Hz), and computational utility. Our results demonstrate that biological Hamiltonian dynamics achieve **superior dynamic stability** and a **3.1x thermodynamic efficiency advantage** over discrete digital baselines. However, we identify a critical “Readout Gap”: while the system forms stable, energy-minimized synchronization manifolds capable of protecting information, standard linear regression fails to decode this phase-encoded memory ($MC \approx 0$). This finding suggests that biological “memory” is physically instantiated as Hamiltonian energy minimization, but its extraction requires non-linear, phase-aware readout mechanisms distinct from those used in von Neumann architectures.