Quantum-like behavior without quantum physics II. A quantum-like model of neural network dynamics.

In earlier work, we laid out the foundation for explaining the quantum-like behavior of neural systems in the basic kinematic case of clusters of neuron-like units. Here we extend this approach to networks and begin developing a dynamical theory for them. Our approach provides a novel mathematical foundation for neural dynamics and computation which abstracts away from lower-level biophysical details in favor of information-processing features of neural activity. The theory makes predictions concerning such pathologies as schizophrenia, dementias, and epilepsy, for which some evidence has accrued. It also suggests a model of memory retrieval mechanisms. As further proof of principle, we analyze certain energy-like eigenstates of the 13 three-neuron motif classes according to our theory and argue that their quantum-like superpositional nature has a bearing on their observed structural integrity.

Quantum-like behavior without quantum physics I : Kinematics of neural-like systems.

Recently there has been much interest in the possible quantum-like behavior of the human brain in such functions as cognition, the mental lexicon, memory, etc., producing a vast literature. These studies are both empirical and theoretical, the tenets of the theory in question being mainly, and apparently inevitably, those of quantum physics itself, for lack of other arenas in which quantum-like properties are presumed to obtain. However, attempts to explain this behavior on the basis of actual quantum physics going on at the atomic or molecular level within some element of brain or neuronal anatomy (other than the ordinary quantum physics that underlies everything), do not seem to survive much scrutiny. Moreover, it has been found empirically that the usual physics-like Hilbert space model seems not to apply in detail to human cognition in the large. In this paper we lay the groundwork for a theory that might explain the provenance of quantum-like behavior in complex systems whose internal structure is essentially hidden or inaccessible. The approach is via the logic obeyed by these systems which is similar to, but not identical with, the logic obeyed by actual quantum systems. The results reveal certain effects in such systems which, though quantum-like, are not identical to the kinds of quantum effects found in physics. These effects increase with the size of the system.