REVIEW 3 major objections 3 minor
Measuring the entropy of a neuron cell from its membrane current signal
T0 review · 3 major / 3 minor · reviewed 2026-08-06 · deepseek-v4-flash
Pith's one-line read This paper claims that two modified entropy measures make neuron membrane-current entropy peak at the ionic Nernst equilibrium potential, with validation on the logistic map.
desk verdict The entropy peak is claimed after the estimators were modified to produce it, so the abstract's evidence is largely circular; the logistic-map check cannot rescue it. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The argument is carried by two entropy estimators applied to membrane ion current recordings: sample entropy, a regularity statistic that measures how unpredictable a signal is, and scalogram entropy, the Shannon entropy of the wavelet energy distribution across scales. Their reference point is the Nernst equilibrium potential $E_{\mathrm{Nernst}} = \frac{RT}{zF}\ln\frac{[X]_\mathrm{out}}{[X]_\mathrm{in}}$ of the permeant ion, the voltage at which electrical and concentration gradients balance. The paper proposes two modifications to these estimators so that their output peaks when the membrane potential sits at that equilibrium potential, and validates the modified estimators on the logistic map $x_{n+1}=r x_n(1-x_n)$, where entropy results can be compared with Lyapunov exponents.
What would settle it
Record membrane currents from a neuron under voltage-clamp while stepping the membrane potential across the predicted Nernst potential for the dominant ion and measure the reversal potential from the current-voltage relationship; if the modified entropy does not peak at that measured reversal potential, and does not shift when extracellular ion concentrations are changed to move the Nernst potential, the central claim is false.
Extended reading notes
Core claim
The central claim is that, after two modifications to the sample entropy and scalogram entropy calculations, entropy values computed from membrane ion current signals of mouse mPFC neurons peak near the Nernst equilibrium potential of the ions, matching the thermodynamic expectation that entropy is maximal at equilibrium. The modified approaches were validated on the logistic map, and the entropy results were compared with Lyapunov exponents. The paper concludes that entropy measurements can be used to analyze the behavior of living cells and may detect differences between tumor and normal cells or the effects of drugs on cells.
Load-bearing premise
The whole approach rests on the premise that a living neuron's electrical activity should reach maximum entropy exactly at the Nernst equilibrium potential of its ions, and that ordinary entropy methods fail to show this because of a measurement flaw rather than because the premise is wrong.
Editorial extensions
If this is right
- The modified entropy measures peak at the Nernst equilibrium potential, so entropy computed from membrane current tracks the ionic equilibrium state of a neuron.
- Entropy measurements can be used to analyze the behavior of living cells, as the paper concludes.
- The method could detect differences between the behavior of tumor and normal cells.
- The method could detect the effects of drugs on cells.
- The comparison with Lyapunov exponents indicates that entropy and chaotic-instability measures agree on the dynamical state of the signal.
Reading between the lines
- Because the modifications were introduced specifically to move the entropy peak to the Nernst potential, the logistic-map validation mainly shows internal consistency; an independent check would test real neurons with altered ion gradients.
- Once the two modifications are specified, a clean test is to apply them to synthetic ion-current signals with known reversal potentials and check that the entropy peak tracks the target.
- The same idea could be tested with other signal-entropy estimators, such as permutation entropy or approximate entropy, to see whether the Nernst-peak property is specific to sample and scalogram entropy or generalizes across entropy measures.
Signed reviews
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript claims that entropy measurements of membrane ion currents from mouse mPFC neurons, using sample entropy and scalogram entropy, can be modified so that entropy peaks at the Nernst equilibrium potential of the ions. The authors state that traditional calculations did not show this peak, so they introduced two modifications specifically designed to make the entropy maximum coincide with the ionic equilibrium. They report that the modified methods indeed produce a peak around the equilibrium potential and that the approaches were validated using the logistic map, with comparisons to Lyapunov exponents. The abstract contains no quantitative results, no statistical analysis, no description of the modifications, and no independent validation of the core claim.
Significance. If it were established that entropy estimators peak at the Nernst equilibrium potential in a way that is not forced by construction, the work could offer a useful tool for characterizing cellular states and could have translational implications for tumor versus normal cell discrimination or drug effects. However, as presented, the central claim is built on modifications explicitly introduced to produce the observed peak, so the reported agreement with the Nernst potential is expected by design rather than evidence for a genuine entropy law. The logistic-map validation is unrelated to membrane currents or ionic equilibrium and therefore cannot anchor the specific biological claim. The potential significance is real but the current evidence does not support it.
major comments (3)
- [Abstract, first and third sentences] The abstract states that 'two modifications to these measurement methods were proposed to adjust the entropy value to the maximum at the equilibrium potential of the ions.' This wording indicates that the modifications were chosen to force the entropy peak to coincide with the Nernst potential. Observing a peak at the equilibrium potential after such tuning is a circular confirmation, not a measurement result. The authors need to show that the modifications are derived from independent theoretical principles or that they recover known entropy maxima in systems where the true maximum is not the Nernst potential.
- [Abstract, validation sentence] The validation using the logistic map is not evidence for the cellular claim. The logistic map has no ion currents, no membrane potential, and no Nernst equilibrium potential, so it cannot test whether the modified entropy methods correctly locate the ionic equilibrium in a neuron. Unless the logistic-map experiment includes a synthetic signal with a known and independently defined equilibrium potential, the observed peak alignment remains unvalidated.
- [Abstract overall] The abstract provides no numerical results, no sample sizes, no error bars, no statistical comparisons, and no description of the two modifications. For a claim that traditional entropy calculations fail and modified calculations succeed, the absence of quantitative evidence makes the central assertion unverifiable. The authors need to report the modification rules, the data analysis pipeline, and a statistical test of whether the entropy peak is significantly aligned with the Nernst potential across cells and ion species.
minor comments (3)
- [Abstract, introduction sentence] The statement that 'the entropy increases in the direction of the movement of the system towards the equilibrium' is a rough paraphrase of thermodynamic entropy production, but its application to sample entropy and scalogram entropy of a membrane current signal is not self-evident and deserves a precise definition and supporting reference.
- [Abstract, concluding sentences] The claims about detecting differences between tumor and normal cells or drug effects are speculative and not supported by any data in the abstract; these statements should be framed as future directions, not as results.
- [Abstract, 'Nernst equilibrium potential' clause] The phrase 'the entropy is expected to reach a maximum at the moment when the membrane potential reaches the Nernst equilibrium potential' is not justified by standard thermodynamics, where equilibrium is a state of maximum total entropy of the system plus environment, not necessarily a maximum of a single empirical entropy estimator computed from one observable. The authors should clarify the theoretical basis for this expectation.
Circularity Check
Entropy peak at Nernst potential is built into the proposed modifications, not discovered.
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fitted input called prediction
[Abstract (sentence introducing the two modifications and reporting the result)]
"Therefore, two modifications to these measurement methods were proposed to adjust the entropy value to the maximum at the equilibrium potential of the ions. As a result of these proposed modifications, the entropy values were observed to peak around the equilibrium potential of the ions."
The modifications are explicitly designed to place the entropy maximum at the Nernst equilibrium potential. The subsequent observation that the modified entropy peaks near that potential is therefore forced by the construction of the estimators, not an independent empirical confirmation. The abstract reports no derivation of the modifications from a free-standing principle and no test on a system where the true entropy maximum is known to be elsewhere. The agreement is a restatement of the adjustment target, making the claimed validation circular.
full rationale
The central claim is that two modified entropy measures peak at the Nernst equilibrium potential. The abstract states the modifications were proposed 'to adjust the entropy value to the maximum at the equilibrium potential of the ions,' which means the target is imposed on the estimators. Observing the peak afterwards is expected by construction. The logistic-map validation does not break the circularity: the logistic map has no ion currents and no Nernst potential, so it cannot validate the specific alignment of the entropy peak with an ionic equilibrium. No independent synthetic or biological benchmark is reported where the true entropy maximum differs from the Nernst potential, so the claim is not exposed to falsification. The paper also relies on an unproven assumption that entropy must peak exactly at the Nernst potential, which is the premise the modifications enforce. Score 6 reflects that the central 'prediction' reduces partly to the design goal, while the entropy methods themselves may have some independent content.
Assumptions & free parameters
free parameters (1)
- Entropy modification parameters (two modifications) =
Not reported in abstract
assumptions (3)
- domain assumption Entropy increases as a system moves toward equilibrium.
- domain assumption The Nernst equilibrium potential is the correct reference for the entropy peak of ion currents.
- domain assumption Sample entropy and Scalogram entropy are valid measures of neuronal membrane current entropy.
Cite this review
Pith. "Pith review of Measuring the entropy of a neuron cell from its membrane current signal." pith.science (2026). https://pith.science/paper/CMZTS42S
@misc{pith2026250800968,
author = {Pith},
title = {Pith review of: Measuring the entropy of a neuron cell from its membrane current signal},
year = {2026},
howpublished = {\url{https://pith.science/paper/CMZTS42S}},
note = {Machine review of arXiv:2508.00968}
}
read the original abstract
The purpose of this study was to investigate how the entropy of a neuron cell can be measured using membrane ion current signals, which were recorded from neurons in the mouse medial prefrontal cortex (mPFC). The sample entropy and the Scalogram entropy were used as entropy measurement methods. It is well known that the entropy increases in the direction of the movement of the system towards the equilibrium. Therefore, in the process of the electrical activity of a living cell, the entropy is expected to reach a maximum at the moment when the membrane potential reaches the 'Nernst equilibrium potential' (or ionic equilibrium) of the ions. However, it was observed that the entropy values obtained by traditional calculations did not reach the peak at the equilibrium state of the ions. Therefore, two modifications to these measurement methods were proposed to adjust the entropy value to the maximum at the equilibrium potential of the ions. As a result of these proposed modifications, the entropy values were observed to peak around the equilibrium potential of the ions. These refined approaches were successfully validated using the Logistic map. Additionally, the entropy results were compared with Lyapunov exponents. The results show that the behaviour of living cells can be analysed using entropy measurements. The results also suggest that the method could be used to detect differences in the behaviour of tumour and normal cells, or the effects of drugs on cells.
Reviewed August 6, 2026 · model on record in the stance chip above.
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