Biochemical basis of Quantum-like neuronal dynamics

The nervous system is a complex dynamical system that incorporates higher order biology (e.g., multicellular architecture) and lower-order biology (e.g., intra cellular pathway) that can be modeled via classical laws such as reaction-diffusion models. Simple reaction-diffusion models of neuronal tissue are shown to support bio-chemical wave effects that are analogous to quantum phenomena. These phenomena include quantum-like superpositions and classical entanglement which will not be affected by decoherence n the wet and warm brain environment. These classical phenomena could enable quantum-like complexity of brain functions. Conventional reaction-diffusion models of biological tissues challenge the current quantum brain hypothesis and suggest that the brain should perhaps be thought of as a classical quantum-like system. Statement of Significance: This manuscript introduces the notion of nonseparability (classical entanglement) in the case of biochemical waves in arrays of coupled axons. We use a linear reaction-diffusion model with cross diffusion to address nonseparability between degrees of freedom (along and across the axon array). Perturbation theory applied to a nonlinear model with quadratic nonlinearity is used to illustrate nonseparability between modes along the axons. This paper suggests that the brain should perhaps be thought of as a classical quantum-like system.