Brain functions emerge as thermal equilibrium states of the connectome

TL;DR

This paper introduces an algebraic quantum model that links brain structural connectomes to emergent functions, demonstrating how neural networks reach thermal equilibrium states that underpin cognition and behavior.

Contribution

The paper presents a novel algebraic quantum framework connecting structural connectomes to brain functions, using KMS states to model neural activity and introduce the Integration Capacity index.

Findings

Brain functions emerge as thermal equilibrium states of the connectome.

The model predicts how network topology influences cognition and behavior.

Application to C. elegans connectome demonstrates the approach's validity.

Abstract

A fundamental idea in neuroscience is that cognitive functions -- such as perception, learning, memory, and locomotion -- are shaped and constrained by the brain's structural organization. Despite significant progress in mapping and analyzing structural connectomes, the principles linking the brain's physical architecture to its functional capabilities remain elusive. Here, we introduce an algebraic quantum model to bridge this theoretical gap, offering new insights into the relationship between the connectome and emergent brain functions, while connecting structural data to functional predictions. Using the well-mapped C. elegans anatomical and extrasynaptic connectomes, we demonstrate that brain functions, defined as functional networks of a neural system, emerge as thermal equilibrium states of an algebraic quantum system derived from the graph algebra of the underlying directed multigraph. Specifically, these equilibrium states, characterized by the Kubo-Martin-Schwinger (KMS) formalism, reveal how individual neurons contribute to functional network formation. Our model illuminates the structure-function relationship in neural circuits through two key features: (1) a functional connectome that delineates topologically driven neuronal interactions and (2) an Integration Capacity (IC) index that quantifies how effectively neurons coordinate and modulate diverse information flows. Together, these features provide a statistical and mechanistic account of information flow and reveal how the network topology of the connectome predicts cognition and complex behaviors.