# The Heat of Nervous Conduction: A Thermodynamic Framework

## TL;DR

This paper presents a thermodynamic model of nerve conduction, showing that surface charge density and electrical energy changes explain the observed heat signatures during neural activity.

## Contribution

It introduces a detailed electrostatic model that refines the Condenser Theory, quantifying heat production and absorption based on membrane surface charges and energy changes.

## Key findings

- The model predicts heat signatures consistent with experimental data.
- Surface charge bias of 0.05 C/m² explains heat magnitude.
- Electrical energy change is the primary heat mechanism during nerve conduction.

## Abstract

Early recordings of nervous conduction revealed a notable thermal signature associated with the electrical signal. The observed production and subsequent absorption of heat arise from physicochemical processes that occur at the cell membrane level during the conduction of the action potential. In particular, the reversible release of electrical energy stored as a difference of potential across the cell membrane appears as a simple yet consistent explanation for the heat production, as proposed in the "Condenser Theory." However, the Condenser Theory has not been analyzed beyond the analogy between the cell membrane and a parallel-plate capacitor, i.e. a condenser, which cannot account for the magnitude of the heat signature. In this work, we use a detailed electrostatic model of the cell membrane to revisit the Condenser Theory. We derive expressions for free energy and entropy changes associated with the depolarization of the membrane by the action potential, which give a direct measure of the heat produced and absorbed by neurons. We show how the density of surface charges on both sides of the membrane impacts the energy changes. Finally, considering a typical action potential, we show that if the membrane holds a bias of surface charges, such that the internal side of the membrane is 0.05 C m$^{-2}$ more negative than the external side, the size of the heat predicted by the model reaches the range of experimental values. Based on our study, we identify the change in electrical energy of the membrane as the primary mechanism of heat production and absorption by neurons during nervous conduction.