Quantum π in Biomolecular Dynamics: Proteins as Nano-Quantum Fluids

I propose a theoretical framework in which proteins are treated as nano-scale quantum fluids, whose internal dynamics are described by a Quantum π-field defined on their three-dimensional structure. Building on the hydrodynamic formulation of quantum mechanics (Madelung quantum hydrodynamics), I introduce a π-field that encodes local quantum coherence, phase topology, and energy flow within the protein, with particular emphasis on aromatic networks and electron/proton transfer channels. In this picture, proteins are not merely static folded structures or classical particles diffusing on an energy landscape; instead, they become quantum-coherent, fluid-like entities, with internal flows, vortices, and topological defects. Mutations and ligand binding are modeled as perturbations of the π-field, modifying local coherence, transport efficiency, and long-range allosteric communication. This approach unifies concepts from quantum hydrodynamics, protein energy landscapes, and bio-inspired quantum information flows, and it suggests a new class of computational tools for predicting mutation effects, functional hotspots, and dynamical pathways. To my knowledge, no existing biomolecular theory explicitly treats proteins as nano-quantum fluids governed by a π-field. I therefore present this framework as a novel conceptual and mathematical model for biomolecular dynamics.