Thermodynamic neural networks and intersection theory: an ontological hypothesis of emergent intelligence

This article proposes a new ontological framework for describing cognitive processes, grounded in intersection theory and an entropy-based model of the space of truths. At the micro-level, we show that neurons and neuronal populations function as thermodynamic systems that reside in regimes of fluctuations, relaxations, and entropic transitions. At the macro-level, these processes manifest as ordered structures-the topologies of truths and their intersections-that jointly shape the cognitive landscape. We introduce the notion of ontological truth as the minimal quantum of reality, as well as the epistemic agent (individual or collective) who performs septation (partitioning), dividing the universal space of truths into known and unknown zones. On this basis, we formulate the entropic trajectory of cognition, which characterizes the evolving balance between the known and the unknown over time. We further show that synchronization of individual agents via the operator of temporal velocity [Formula: see text] yields a collective agent whose entropy is defined as a coherent integration of the entropies of its constituent agents. This construction scales from sensory physiology (receptors as individual agents) to the collective cognition of humanity as a whole. At the concluding level, we introduce the key notion of epistemic bifurcation (splitting)-the multiplicity of individual reconstructions of the same ontological truth-which explains why collective cognition is not a mere sum of private representations but acquires the quality of emergent integration. Taken together, the article demonstrates that cognitive topology is an emergent reflection of thermodynamic dynamics, and that a universal scheme of intersections provides a unified ontological language for processes ranging from the micro-physiology of neurons to macro-level epistemology and the history of civilization.

The online version contains supplementary material available at 10.1007/s11571-026-10438-y.