Entropic Brain Hypothesis Overview

• Entropic Brain Hypothesis is a framework linking spontaneous neural entropy with the diversity and richness of conscious states, as observed in altered conditions like psychedelia.
• It employs metrics such as Shannon entropy, Lempel–Ziv complexity, and network-distribution entropy to quantify variations in neural dynamics.
• Recent studies refine EBH by differentiating between raw entropy and complexity, thereby addressing conflicting findings in high-content versus minimal conscious states.

The Entropic Brain Hypothesis (EBH) is a model of conscious processes that regards the entropy of spontaneous brain activity as a marker of “phenomenal richness.” In its original psychedelic framing, it proposes that psychedelic states, described as “primary consciousness,” are characterized by higher entropy in the brain’s functional organization than the normal waking state, described as “secondary consciousness” (Viol et al., 2016). In this formulation, higher entropy is loosely equivalent to a richer, more variable repertoire of functional connectivity patterns, and classical psychedelic states constitute the canonical empirical support for the hypothesis. Subsequent work has both extended and challenged this framework: one line places EBH in a nonadditive statistical-mechanics setting using the Tsallis entropic index $q$ and $q$-Gaussian EEG statistics (Lima et al., 2 May 2026), while another argues that entropy alone cannot resolve differences between high-content psychedelic experiences and Minimal Phenomenal Experiences, proposing complexity as the more appropriate index of phenomenal richness (Mago et al., 15 May 2026). Recent EEG work on self-induced trance states further indicates that altered states can involve mixed directional changes across entropy, complexity, and aperiodic metrics rather than a uniformly elevated “entropic” profile (Oswald et al., 23 Sep 2025).

1. Conceptual formulation and operational definitions

In the EBH, “brain entropy” is taken as a proxy for the potential information carried by spontaneous neural activity. The core intuition is stated as a sequence of linked propositions: phenomenal experience carries informational content; richer experiences possess more content; neural dynamics instantiate information processing; therefore richer experiences should correlate with higher entropy in spontaneous neural activity (Mago et al., 15 May 2026). This framework was originally motivated by psychedelic phenomenology, especially reports of expanded awareness, heightened cognitive flexibility, and novel associations.

Operationally, the term “brain entropy” has not been restricted to a single metric. Common operationalizations in human neuroimaging include Shannon entropy of a discretized BOLD time series,

$H = -\sum_i p_i \log p_i,$

where $p_i$ is the empirical probability of observing the $i$-th amplitude or state; Lempel–Ziv complexity (LZc), which estimates signal compressibility by counting distinct substrings; and spectral entropy,

$H_{\mathrm{spectral}} = -\int P(f)\log P(f)\,df,$

computed from the normalized power spectral density $P(f)$ (Mago et al., 15 May 2026). In the Ayahuasca network study, the relevant entropy is instead the Shannon entropy of the degree distribution of a whole-brain functional network,

$H[P] = -\sum_k P(k)\ln P(k),$

with $P(k)$ denoting the fraction of nodes with degree $k$ (Viol et al., 2016).

A persistent source of ambiguity in the EBH literature is that these measures are related but non-identical. Shannon entropy, spectral entropy, LZc, and network-distribution entropy quantify different statistical properties of neural activity or connectivity. This suggests that EBH is better understood as a family of empirically testable claims about increased variability, diversity, or dispersion in neural dynamics under particular conscious states, rather than as a theorem tied to a single estimator.

2. Whole-brain network implementation in the Ayahuasca study

A direct network-theoretic test of EBH was carried out by Viol et al. using resting-state fMRI before and after ingestion of Ayahuasca, a psychedelic beverage of Amazonian indigenous origin with legal status in Brazil in religious and scientific settings (Viol et al., 2016). Each subject’s brain was parcellated into $q$0 anatomical regions using the Harvard–Oxford atlas. For each pair of regions $q$1, the Pearson correlation $q$2 was computed from resting-state fMRI time series band-pass filtered to $q$3 Hz via a Daubechies wavelet. A binary, undirected adjacency matrix $q$4 was then obtained by thresholding $q$5, with $q$6 if linked and $q$7 otherwise. The threshold $q$8 was chosen so that the resulting networks were sparse, with mean degree $q$9 between 24 and 39, fully connected, and sharing small-world properties.

Within this construction, the degree of node $H = -\sum_i p_i \log p_i,$0 is

$H = -\sum_i p_i \log p_i,$1

and the degree distribution $H = -\sum_i p_i \log p_i,$2 is the fraction of nodes having degree $H = -\sum_i p_i \log p_i,$3. Network integration was quantified through geodesic distance,

$H = -\sum_i p_i \log p_i,$4

where $H = -\sum_i p_i \log p_i,$5 is the shortest-path length from $H = -\sum_i p_i \log p_i,$6 to $H = -\sum_i p_i \log p_i,$7; global efficiency,

$H = -\sum_i p_i \log p_i,$8

and the local efficiency $H = -\sum_i p_i \log p_i,$9 and clustering coefficient $p_i$0, which quantify how well neighbors of a node communicate when that node is removed.

The experimental design comprised 10 healthy, right-handed adult volunteers with mean age 31.3 years, all experienced in Ayahuasca use for at least five years and at least twice per month. One subject was excluded for motion and two more were excluded for lack of a common network-density window, leaving $p_i$1 for the main analysis. Scanning used a 1.5 T Siemens Magneton and resting-state EPI–BOLD with $p_i$2 ms, $p_i$3 ms, voxel size $p_i$4, and 150 volumes, plus $p_i$5-weighted anatomical imaging. Each subject was scanned twice: in an ordinary eyes-closed resting condition and 40 minutes after drinking $p_i$6 Ayahuasca, approximately 200 mL total, containing $p_i$7 DMT and $p_i$8 harmine. Preprocessing included slice-timing correction, motion correction with 6 regressors, spatial smoothing at 5 mm FWHM, signal regression for white matter, CSF, and global signal, and nonlinear normalization to MNI152.

This implementation is important because it operationalized EBH at the level of whole-brain functional complex networks rather than only within univariate signal statistics. It therefore linked the hypothesis to graph-theoretic changes in the organization of resting-state functional connectivity.

3. Quantitative findings: increased degree-distribution entropy and rebalanced integration

The central empirical result of the Ayahuasca study is that the Shannon entropy of the degree distribution rises systematically after Ayahuasca ingestion across all mean-degree thresholds $p_i$9 (Viol et al., 2016). The degree-distribution shape also changes: its variance increases and its kurtosis decreases, indicating a broader, flatter degree histogram. Subject-by-subject boxplots show, for each of the 7 subjects, a significant increase in $i$0 with paired $i$1-test $i$2. A typical magnitude reported in the summary is $i$3 nats and $i$4 nats, corresponding to an approximately 10% increase in uncertainty of degree.

The same analysis also identified a specific redistribution of network integration. Geodesic distance $i$5 increases and global efficiency $i$6 decreases under Ayahuasca, whereas clustering coefficient $i$7 and local efficiency $i$8 both increase. These changes do not all have the same explanatory status. Comparison with Maslov-randomized iso-entropic networks shows that the altered degree distribution does not by itself account for the observed shifts in $i$9 and $H_{\mathrm{spectral}} = -\int P(f)\log P(f)\,df,$0; the randomized counterparts do not exhibit the same changes. By contrast, the changes in $H_{\mathrm{spectral}} = -\int P(f)\log P(f)\,df,$1 and $H_{\mathrm{spectral}} = -\int P(f)\log P(f)\,df,$2 are largely accounted for by the broadened $H_{\mathrm{spectral}} = -\int P(f)\log P(f)\,df,$3, since the iso-entropic randomized networks show nearly the same $H_{\mathrm{spectral}} = -\int P(f)\log P(f)\,df,$4 and $H_{\mathrm{spectral}} = -\int P(f)\log P(f)\,df,$5. Paired-sample $H_{\mathrm{spectral}} = -\int P(f)\log P(f)\,df,$6-tests on $H_{\mathrm{spectral}} = -\int P(f)\log P(f)\,df,$7, $H_{\mathrm{spectral}} = -\int P(f)\log P(f)\,df,$8, $H_{\mathrm{spectral}} = -\int P(f)\log P(f)\,df,$9, $P(f)$0, and $P(f)$1 yield $P(f)$2, often $P(f)$3, across almost all $P(f)$4 values.

The interpretation offered in the study is that increased $P(f)$5 implies a more diverse repertoire of network hubs and a less constrained functional architecture, while decreased global efficiency suggests that large-scale broadcast of information becomes less efficient and increased local integration may underlie intensified within-module processing (Viol et al., 2016). This suggests that the EBH, in this network formulation, is not only a claim about larger entropy values but also about a rebalancing between global and local integration in psychedelic states.

4. Nonadditive entropic extensions and criticality-based interpretations

A more recent extension places EBH in the framework of nonadditive entropies appropriate for complex systems (Lima et al., 2 May 2026). In this setting, the Tsallis entropy for a discrete probability set $P(f)$6 is

$P(f)$7

with composition rule for two independent systems $P(f)$8 and $P(f)$9,

$H[P] = -\sum_k P(k)\ln P(k),$0

Maximizing $H[P] = -\sum_k P(k)\ln P(k),$1 under appropriate constraints yields the $H[P] = -\sum_k P(k)\ln P(k),$2-Gaussian

$H[P] = -\sum_k P(k)\ln P(k),$3

where

$H[P] = -\sum_k P(k)\ln P(k),$4

Here $H[P] = -\sum_k P(k)\ln P(k),$5 is the entropic index controlling tail thickness and $H[P] = -\sum_k P(k)\ln P(k),$6 sets the inverse width.

Lima et al. fit EEG amplitudes to $H[P] = -\sum_k P(k)\ln P(k),$7-Gaussians after band-pass filtering from 0.5 to 100 Hz, applying notch filters at 60 Hz harmonics, zero-meaning each channel, clipping $H[P] = -\sum_k P(k)\ln P(k),$8, segmenting into stationary windows, and normalizing each window so the fluctuation $H[P] = -\sum_k P(k)\ln P(k),$9 has unit standard deviation $P(k)$0. For a trial value of $P(k)$1, they plot

$P(k)$2

perform a weighted linear regression through the origin, and take the slope $P(k)$3 as $P(k)$4. Sweeping $P(k)$5 over an interval $P(k)$6 and choosing the value that maximizes $P(k)$7 yields a best-fit pair $P(k)$8 for each segment, channel, and subject.

Empirically, for each channel $P(k)$9, they find

$k$0

with $k$1 slowly varying from channel to channel. As $k$2, $k$3 with $k$4, and when data from all 17 channels and both subject groups are collapsed by plotting $k$5 versus $k$6, all points fall on the same straight line, which the authors describe as a hallmark of universality and critical-like scaling. In group comparisons, Table I reports

$k$7

with a two-sample $k$8-test yielding $k$9.

Within this interpretation, $q$00 corresponds to purely Gaussian statistics and $q$01 to heavy tails and enhanced fluctuations; variations in $q$02 are then taken to map onto the brain’s proximity to a critical entropic state (Lima et al., 2 May 2026). A plausible implication is that EBH can be reformulated not only as an increase in additive Shannon entropy, but also as a shift in the statistical class of neural fluctuations toward non-Gaussian, critical-like regimes.

5. The entropy–content conundrum and the Complex Brain Hypothesis

The most direct conceptual challenge to EBH arises from Minimal Phenomenal Experiences (MPEs), defined as states in which wakefulness is preserved but phenomenal content is low or absent (Mago et al., 15 May 2026). According to the summary of Mago et al., neuroimaging and EEG studies of MPEs induced by meditation, and possibly 5-MeO-DMT, suggest that these states also show increased neurophysiological entropy, including elevated neural signal diversity and spectral measures of entropy. This creates an “entropy–content conundrum”: the EBH’s monotonic mapping between phenomenal richness and neural entropy cannot easily accommodate the fact that both high-content psychedelic experiences (HCPEs) and low-content MPEs may show elevated entropy relative to baseline wakefulness.

The proposed resolution is the Complex Brain Hypothesis (CBH), which distinguishes entropy from complexity. In this proposal, entropy of neural states, $q$03, measures the dispersion or width of the neural probability distribution, whereas complexity of inference is identified with the relative entropy between posterior and prior beliefs,

$q$04

Under the variational Free Energy Principle, free energy is decomposed as

$q$05

Complexity thus indexes how much posterior beliefs diverge from prior beliefs in order to explain sensory data. The same proposal also cites Integrated Information, $q$06, and the Perturbational Complexity Index (PCI) as alternative complexity measures.

CBH posits two inferential regimes associated with relaxation of high-level prior precision. In a fine-grained or overfitting regime corresponding to HCPEs, priors are relaxed while likelihood precision remains high; the generative model overfits sensory fluctuations, recruits many parameters, and produces proliferation of content, implying high $q$07 and high complexity. In a coarse-grained or underfitting regime corresponding to MPEs, both prior and sensory precision are attenuated, so the generative model collapses to a low-dimensional description; posterior and prior remain close, implying low $q$08 and low complexity despite high residual variability and high entropy. Mago et al. further relate this distinction to algorithmic-information concepts through Kolmogorov complexity,

$q$09

and Minimum Description Length,

$q$10

On this account, EBH is refined rather than discarded. Mago et al. preserve the claim that relaxing high-level priors increases entropy, but argue that phenomenal richness is indexed by complexity rather than entropy alone (Mago et al., 15 May 2026). This suggests that entropy is a marker of liberated or less constrained dynamics, whereas richness depends on whether those liberated dynamics are recruited into a high-dimensional inferential model or absorbed into a coarse-grained, contentless one.

6. Heterogeneous altered states, empirical constraints, and current scope

Recent EEG work on Auto-Induced Cognitive Trance (AICT) illustrates why the empirical scope of EBH remains contested (Oswald et al., 23 Sep 2025). In that study, 27 trained participants underwent 256-channel EEG during rest and self-induced trance. The analysis examined the aperiodic $q$11 spectral exponent, Lempel–Ziv complexity, and sample entropy from source-reconstructed time series parcellated into 300 Yeo atlas ROIs. The power spectrum was modeled as

$q$12

or equivalently in log–log space,

$q$13

LZC was computed after median-split symbolization with default Neurokit2 parameters $q$14 and embedding dimension $q$15, and sample entropy was computed as

$q$16

with $q$17, $q$18, and $q$19.

The principal findings were not a uniform increase in entropy-related metrics. During AICT there was a global reduction in the aperiodic exponent $q$20, with group means of approximately $q$21 at rest and $q$22 in AICT; an overall decrease in mean cortical LZC from approximately $q$23 to $q$24; and a widespread reduction in mean sample entropy from approximately $q$25 to $q$26. Source localization identified decreases in $q$27 in left DLPFC, bilateral dorsomedial PFC and anterior cingulate, posterior cingulate cortex, and left temporo-occipital junction; LZC decreases in left inferior parietal lobule and bilateral middle frontal gyrus; and sample entropy decreases in left superior parietal lobule, left occipital-parietal junction, and additional bilateral occipital and sensorimotor clusters. A random-forest classifier distinguished rest from AICT with 65% ± 10% accuracy for the $q$28 exponent, 68% ± 11% for LZC, 70% ± 10% for sample entropy, and 71% ± 13% for the combined 900-feature model.

The interpretation given in that study is explicitly “contrary to the ‘more entropy = richer conscious experience’ tenet of the Entropic Brain Hypothesis”: AICT exhibits regional decreases in complexity and entropy in posterior parietal areas implicated in sensory integration and agency, while frontal increases in complexity noted in LZC maps alongside reduced $q$29 may index enhanced information integration and conscious access in prefrontal hubs (Oswald et al., 23 Sep 2025). The same study also reports that no explicit multiple-comparison correction was described for ROI-level tests. Taken together with the small-$q$30 main analysis of the Ayahuasca network study and the theoretical challenge posed by MPEs, this indicates that EBH should not be interpreted as a universally monotonic law across all altered states and all entropy-related estimators.

At present, the most defensible encyclopedic characterization is that EBH remains a productive but non-exhaustive framework for relating conscious state changes to increased diversity, variability, or dispersion in neural dynamics. It is directly supported by whole-brain functional-network evidence in a psychedelic state (Viol et al., 2016), extended through nonadditive entropic and criticality-based analyses (Lima et al., 2 May 2026), and substantially refined by arguments that complexity, perturbational responsiveness, and inferential grain must be considered alongside entropy to explain the full range of conscious states (Mago et al., 15 May 2026).