Thermodynamic Insights into Axonal Signaling: A Unified Electro-Thermal Framework

Nerve impulse propagation, a cornerstone of neuronal communication, involves a complex interplay of electrical, thermal, and thermodynamic processes. While the Hodgkin-Huxley (H&H) model provides a foundational understanding of action potentials, it neglects key thermodynamic aspects such as energy dissipation and entropy production. To address this limitation, we develop a novel, thermodynamically consistent electro-thermal model of axonal conduction. This model rigorously couples the Telegrapher's equations (derived from Maxwell's equations) with a derived heat equation that explicitly incorporates entropy production. Crucially, we present two distinct approaches for handling entropy production: (1) an explicit term in the heat equation, allowing for direct analysis of thermodynamic irreversibility, and (2) embedding entropy production within the transmembrane current, ensuring thermodynamic consistency through energy conservation. Preliminary simulations suggest that thermal effects may increase propagation speed by up to 5% in unmyelinated axons and predict a nonlinear relationship between axon radius and temperature rise during action potential propagation. This modular framework, accommodating various ionic current models and levels of mechanical complexity, provides a robust platform for studying the interplay between electrical, thermal, and thermodynamic dynamics in axonal signaling. Our approach offers new insights into the energetic costs of nerve conduction and lays the foundation for investigating the role of thermodynamic factors in neuronal function and disease, such as the effects of hyperthermia on nerve conduction.