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arxiv: 2605.01629 · v1 · submitted 2026-05-02 · ❄️ cond-mat.stat-mech · physics.data-an· physics.med-ph

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Brain criticality through nonadditive entropic analysis of electroencephalograms

Constantino Tsallis, Dimitri M. Abramov, Henrique Santos Lima

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Pith reviewed 2026-05-08 19:36 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech physics.data-anphysics.med-ph
keywords adhdbetatypicalsubjectsbraincomplexityalongbehavior
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The pith

EEG amplitudes follow q-Gaussian distributions where the entropic index q varies monotonically with β, revealing critical brain behavior and higher complexity in ADHD children than typical ones.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The brain is a complex system with many interacting parts that often does not follow ordinary statistics. Researchers therefore use a generalized form of entropy called nonadditive entropy, which leads to q-Gaussian probability distributions instead of normal Gaussians. These distributions are characterized by an index q that quantifies deviation from standard behavior and a parameter β that controls the width. In this work, the authors fitted q-Gaussians to the probability distributions of EEG signal amplitudes recorded from children. They observed that q changes in a steady, monotonic way as β changes, for both typical children and those with ADHD. The authors take this steady change as a signature that the brain operates near a critical point, where small shifts can produce large effects. They also report that ADHD children exhibit higher average q values, indicating greater complexity in their brain signals compared with typical children. This difference is presented as a possible route toward physics-based biomarkers for psychiatric diagnosis.

Core claim

We show that q tends to monotonically vary with β for both typical and ADHD subjects, thus revealing critical behavior of the brain. Moreover, we verify that ADHD subjects have a higher complexity than the typical ones.

Load-bearing premise

That the probability distributions of EEG amplitudes are well-described by q-Gaussians and that the observed monotonic variation of the fitted q with β constitutes direct evidence of criticality without further controls or alternative models.

Figures

Figures reproduced from arXiv: 2605.01629 by Constantino Tsallis, Dimitri M. Abramov, Henrique Santos Lima.

Figure 1
Figure 1. Figure 1: FIG. 1. Signal segments for the Fz and O1 channels for four arbitrarily chosen patients. view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Curves of ln view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Plot of view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Plot of view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Plot of view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Plot of view at source ↗
read the original abstract

On the grounds of nonadditive entropies -- appropriate for complex systems -- we investigate the electroencephalogram amplitudes of typical and ADHD children. The corresponding probability distributions are $q$-Gaussians, i.e., $\rho(x) \propto e_q^{-\beta x^2} \equiv [1+(q-1) \beta x^2]^{1/(1-q)}$, where $(q,\beta)$ are, respectively, the entropic index characterizing complexity and the inverse width. We show that $q$ tends to monotonically vary with $\beta$ for both typical and ADHD subjects, thus revealing critical behavior of the brain. Moreover, we verify that ADHD subjects have a higher complexity than the typical ones. Consistently, biomarkers for objective phychyatric diagnosis could emerge along this path. We show that $q$ tends to monotonically vary with $\beta$ for both typical and ADHD subjects, thus revealing critical behavior of the brain. Moreover, we verify that ADHD subjects have a higher complexity than the typical ones. Consistently, biomarkers for objective phychyatric diagnosis could emerge along this path.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that nonadditive entropies suit complex systems and on two fitted parameters per distribution; no new entities are introduced.

free parameters (2)
  • q
    Entropic index fitted to each EEG amplitude probability distribution to characterize complexity.
  • β
    Inverse-width parameter fitted to the same distributions.
axioms (1)
  • domain assumption Nonadditive entropies are appropriate for complex systems such as the brain.
    Stated as the grounds for using q-Gaussians on EEG data.

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Reference graph

Works this paper leans on

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