This is how thermodynamics can effect neurons. And this is why dissolving gases into the lipid membrane, like nitrogen in the article, cause change the thermodynamic properties like the heat capacity and retard the solid phase a bit. Light gases increase liquidity. That's the anesthetic effect that reduces firing rates. And that's why local atmospheric pressure matters in gas anesthesia dosing.
It's not that the old hogkin-huxley purely electrical circuit model is "wrong", it's a fine approximation of some effects. But it certainly can't explain the reversible uptake and release of heat during a passing action potential, nor the changes in birefringence and optical scattering, nor why nitrogen can act as an anesthetic like in this case.