As of today (2026), the understanding of neuronal operation remains divergent. As [49] formulated, ”bio-electric and a thermodynamic perspectives” are fighting, mostly in the spirit of ”if the only tool you have is a hammer, you tend to see every problem as a nail”, and discusses ”answerable what-if questions that have been overlooked or purposefully neglected thus far”, without attempting to integrate those disciplinary perspectives. (BTW: that effort would be hopeless: as we discuss, the life-related phenomena happen in the ”nobody’s land”: the ”construction of the living matter” requires dividing processes into pieces and describe them with different physical processes that are interfaced to each other.) By neglecting that ions are ”material points” that also have charge, the cellular phenomena cannot be described in either approach alone, given that they are simultaneously governed by the laws of the two mentioned fields, with many specialties. Furthermore, molecular and enzymatic effects also shape the operation, in most cases adding color to it. Our discussion combines appropriately the two disciplines (not the two perspectives!) in an almost abstract approach, emphasizing also their cooperation, furthermore, at some places mentioning also biochemistry. First, we give an overview (with the intention of providing sufficiently solid background for the audience having not too deep knowledge in physics, thermodynamics, and electricity), and we expand the quantitative details in later chapters with a complete disciplinary underpinning.
As we mentioned, other, more physical (sometimes extreme, sometimes called multi-physics) approaches ”have met with fierce opposition from mainstream neuroscience” [35]. The thermodynamic effects seemingly mask the true causes of neuronal function and lead to a misunderstanding of physiological evidence. We discuss the operation of neurons mainly in electrical terms after deriving an ”equivalent thermodynamical electric field”, we can, by considering the electric repulsion of ions, associate the observed mechanical effects and explain the thermodynamical effects of neuronal operation. We discuss the thermoelectrical, computational, information theoretical, and physiological details in different chapters. In those discussions, we return to the same concepts repeatedly, in von Neumann’s ’zigzag’ way, from different points of view (at different abstraction levels and disciplinary depths).
Again, another approach: over the decades, computational and/or mathematical neuroscience implemented ad hoc mathematical formulas only slightly related to neuronal operation because theoretical neuroscience did not provide the correct scientific background. They forgot the warning that ”the success of the equations is no evidence in favour of the mechanism” [9]; biophysics attempts to find out unestablished mechanisms for the equations. It is not possible to understand even correct experimental observations and to design thoughtful experiments; furthermore, among others, to understand the role of synaptic weights, the formation of AP s, and neuronal information processing, without fixing the scientific background (or providing a wrong background), the misunderstood electric operation and misinterpreted physiological observations; furthermore, the abused concepts of technical computing and information that result in ”technomorph biology”[11]. Moreover, we must introduce non-disciplinary physical laws, maybe a more appropriate name for the idea that E. Schrödinger coined [12].
The ’abstract’ means that we omit the physiological details and focus on the abstracted operating principle, what the function or component wants to implement, why neededs. The ’physical’ means that we put a non-disciplinary physical mechanism behind the different stages of operation. We intend to find the appropriate stages, or the series of dynamic stages, with corresponding transitions. Our method is to omit, per stage, the less important interactions and processes. In some (but not all!) cases, we can reduce the actual stage to a single (dominant ) interaction, described by a single scientific discipline. In other cases, the stages (or their interfaces) have a dominant interaction and a correcting interaction, so we need to invent new procedures. Such multiple simultaneous interaction cases are rarely discussed in science. When discussed in science disciplines, the interaction speeds are considered to be the same, and the related laws are used in their simplified form. This is the only place where our description is ’non-ordinary’: we check whether the omissions leading to the ’ordinary’ laws are legal, and derive our ’non-ordinary’ laws where needed. Those laws are non-ordinary only in the sense that, instead of the ’ordinary’ ones we used to in classical science, we use the correct approximation and abstractions needed ”because the construction is different from anything we have yet tested in the physical laboratory” [12]. Furthermore, they may be ”non-ordinary” also in a mathematical sense.
Textbooks, such as Neuronal dynamics and [24], usually skip the question how the neuron, a piece of living material, is modeled. Instead, they put behind their formulas, without validating them for biology, the picture taken from classical physics, which was validated for different circumstances (non-living material), for describing electrical circuits. This way, they shoot themself in the foot. At the time of setting up their model, it was not known that the overwhelming majority of ion channels were concentrated in the AIS, and only a small fraction is distributed over the membrane’s surface. HH hypothesized that the (at that time, only hypothesized) ion channels are distributed over the membrane, so that the neuron can be modelled as a distributed oscillator circuit, corresponding to a parallelly connected oscillator comprising discrete elements and . Their model was the best possible one in their time, but we know for decades [50, 51, 52, 53, 54], that those ion channels that they hypothesized serve only for maintaining the resting state, and the transient state needs a different mechanism.