The Complex Brain Hypothesis: Resolving the Entropy-Content Conundrum in Minimal Phenomenal Experience

Edmundo Lopez-Sola; Jakub Vohryzek; Jonas Mago; Karl Friston; Michael Lifshitz; Robin Carhart-Harris; Shamil Chandaria

arxiv: 2605.16146 · v1 · pith:4X7K2QLWnew · submitted 2026-05-15 · 🧬 q-bio.NC

The Complex Brain Hypothesis: Resolving the Entropy-Content Conundrum in Minimal Phenomenal Experience

Jonas Mago , Edmundo Lopez-Sola , Jakub Vohryzek , Michael Lifshitz , Robin Carhart-Harris , Karl Friston , Shamil Chandaria This is my paper

Pith reviewed 2026-05-19 18:30 UTC · model grok-4.3

classification 🧬 q-bio.NC

keywords minimal phenomenal experiencecomplex brain hypothesisentropic brain hypothesisbrain complexityentropyconsciousnessmeditationpsychedelics

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The pith

Brain complexity, not entropy, better indexes the difference between minimal and high-content phenomenal experiences.

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

The paper advances the Complex Brain Hypothesis to resolve a puzzle for the Entropic Brain Hypothesis. Recent studies show that minimal phenomenal experiences, such as those in certain meditation states, can exhibit elevated brain entropy even though they lack the rich content seen in psychedelic experiences. The authors argue that complexity, shaped by the grain of inference the brain uses to resolve uncertainty, distinguishes these states: fine-grained inference produces proliferating content while coarse-grained inference yields contentless awareness. A sympathetic reader would care because this distinction preserves the link between entropy and certain altered states while explaining why entropy alone does not track phenomenal richness.

Core claim

The Complex Brain Hypothesis proposes that the richness of experience differentiating MPEs from HCPEs is better indexed by complexity than by entropy. Brain complexity is modulated by the grain of inference through which the brain resolves uncertainty: some HCPEs exemplify a fine-grained regime, in which loosened constraints amplify fluctuations into proliferating content, whereas some MPEs exemplify a coarse-grained regime, in which a simpler model dissolves variety into an experience of 'contentless' awareness. Both regimes can be associated with elevated brain entropy, but they diverge in phenomenology and perturbational signatures.

What carries the argument

The Complex Brain Hypothesis (CBH), which holds that richness of experience is indexed by complexity rather than entropy and is modulated by the grain of inference used to resolve uncertainty.

If this is right

Both minimal and high-content states can exhibit high entropy while differing in their complexity signatures.
Phenomenal richness depends on whether the brain's model operates at a fine or coarse grain of inference.
Perturbational complexity or related measures should differ between MPEs and HCPEs even when entropy is similarly elevated.
MPEs become a key test case that refines rather than contradicts the Entropic Brain Hypothesis.
Computational theories of consciousness must incorporate granularity of inference to explain contentless awareness.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Interventions that shift inference granularity, such as specific meditation techniques, could predictably move a person between minimal and content-rich states.
The framework suggests entropy and complexity should be measured jointly in future studies of altered states to avoid conflating them.
If the distinction holds, it may help explain why some high-entropy states feel empty while others feel filled with content.

Load-bearing premise

That recent neuroimaging studies of meditation-induced and possibly 5-MeO-DMT-induced states show increased neurophysiological entropy, while the Entropic Brain Hypothesis treats entropy as a direct marker of phenomenal richness.

What would settle it

A direct comparison showing that complexity measures fail to differentiate MPEs from HCPEs more effectively than entropy measures do, or that perturbational signatures do not diverge between the two despite matched entropy levels.

Figures

Figures reproduced from arXiv: 2605.16146 by Edmundo Lopez-Sola, Jakub Vohryzek, Jonas Mago, Karl Friston, Michael Lifshitz, Robin Carhart-Harris, Shamil Chandaria.

**Figure 1.** Figure 1: Free energy as a trade-off between complexity and accuracy. The variational free energy F can be decomposed into a complexity term and an accuracy term. Complexity corresponds to the Kullback–Leibler divergence between posterior and prior beliefs, 𝐷{"#}[𝑄(𝑥)||𝑃(𝑥)], and reflects the degree to which posterior beliefs must deviate from prior expectations to account for sensory data. Accuracy corresponds to t… view at source ↗

**Figure 2.** Figure 2: The entropy–content conundrum. The entropic brain hypothesis (EBH) implies a monotonic mapping from phenomenological content to entropy. This would predict that minimal-content states are associated with low entropy while content-rich states are associated with high entropy. However, empirical evidence indicates that both MPEs (e.g., jhāna, 5-MeODMT) and HCPEs (e.g., LSD, psilocybin, N,N-DMT) exhibit elev… view at source ↗

**Figure 4.** Figure 4: Solving the conundrum: complexity, entropy and phenomenal richness. Conceptual illustration of the relationship between model complexity (black), entropy (red), and phenomenal richness. The left panels recapitulate the three regimes of inference in [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗

**Figure 5.** Figure 5: Entropy and complexity in the coffee–cream mixing process (adapted from Aaronson et al., 2014). As black coffee and white cream mix, entropy increases monotonically, reflecting the growing number of particle configurations consistent with the systems state. At coarse-grained scales, however, complexity rises during the formation of structured swirls and then collapses once the mixture becomes uniform, illu… view at source ↗

**Figure 6.** Figure 6: Entropy rises in both HCPEs and absorptive states, but complexity diverges depending on the inferential regime. The red curve depicts the entropy of posterior beliefs or their neuronal parameterization; it increases monotonically as prior constraints are relaxed. The purple curve represents complexity under fine-grained HCPE inference: unattenuated sensory fluctuations are amplified into proliferating cont… view at source ↗

**Figure 7.** Figure 7: Three-dimensional extension of the entropic brain hypothesis. (a) A threedimensional schematic showing how adding a third variable, here labeled wakefulness, separates states with low phenomenal richness and high entropy (MPE) or low entropy (sleep). When this surface is projected onto the two-dimensional plane, the pattern in panel (b) emerges. (b) [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗

read the original abstract

Minimal Phenomenal Experiences (MPEs) are states of consciousness in which wakefulness is preserved but phenomenal content is low or absent. 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', exemplified by high-content psychedelic experiences (HCPEs). Yet recent human neuroimaging studies of MPEs induced by meditation -- and possibly 5-MeO-DMT -- suggest that these states, defined by their phenomenological simplicity, also show signs of increased neurophysiological entropy. This presents a conundrum for the EBH: brain entropy is elevated with increased and decreased richness of the phenomenal experience. Here, we put forward the Complex Brain Hypothesis (CBH), which proposes that the richness of experience differentiating MPEs from HCPEs is better indexed by complexity than by entropy. We argue that brain complexity is modulated by the grain of inference through which the brain resolves uncertainty: some HCPEs exemplify a fine-grained regime, in which loosened constraints amplify fluctuations into proliferating content, whereas some MPEs exemplify a coarse-grained regime, in which a simpler model dissolves variety into an experience of 'contentless' awareness. Both regimes can be associated with elevated brain entropy, but they diverge in phenomenology and perturbational signatures. By resolving the entropy-content conundrum, the CBH refines the EBH and highlights MPEs as an important test case for computational theories of consciousness.

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.

Desk Editor's Note private letter to a colleague

The paper reframes the entropy conundrum by tying phenomenal richness to inference grain and complexity rather than raw entropy, but the move stays qualitative.

read the letter

The main point is that this work introduces the Complex Brain Hypothesis to handle cases where brain entropy rises in both high-content psychedelic states and low-content minimal phenomenal experiences. It keeps the entropy idea but argues that complexity, shaped by whether inference is fine- or coarse-grained, better tracks the difference in felt richness. Coarse-grained regimes in MPEs are said to collapse variety into simple awareness, while fine-grained ones in HCPEs let fluctuations produce more content. Both can show elevated entropy yet diverge in phenomenology and responses to perturbation. That framing is new relative to the earlier Entropic Brain Hypothesis papers from overlapping authors, and it usefully highlights MPEs as a test case for active-inference accounts of consciousness. The authors do a clear job summarizing the conflicting neuroimaging observations from meditation and 5-MeO-DMT studies without overclaiming new data. The limitation is that the link from grain of inference to a concrete complexity measure is never made explicit. No equation, simulation, or mapping to something like multiscale entropy or Lempel-Ziv is supplied, so the dissociation between high entropy and low complexity remains asserted rather than derived. The argument also rests on reinterpreting the group's own prior results, which leaves the circularity concern intact. This is the sort of conceptual paper that fits a reading group focused on computational models of consciousness or psychedelic research. A referee could usefully press for a testable prediction or a minimal formal sketch. I would send it to peer review.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes the Complex Brain Hypothesis (CBH) to resolve an apparent conundrum in the Entropic Brain Hypothesis (EBH). It claims that both minimal phenomenal experiences (MPEs, e.g., from meditation or possibly 5-MeO-DMT) and high-content psychedelic experiences (HCPEs) can exhibit elevated brain entropy, yet differ in phenomenal richness because complexity (not entropy) tracks content; this difference arises from the grain of inference, with coarse-grained regimes in MPEs dissolving variety into contentless awareness and fine-grained regimes in HCPEs amplifying fluctuations into rich content.

Significance. If the proposed dissociation holds, the CBH would usefully refine the EBH by separating entropy from complexity as markers of phenomenal richness and would position MPEs as an important test case for computational theories of consciousness. The manuscript offers a clear conceptual reframing that could guide future perturbational and neuroimaging work, though its strength currently rests on reinterpretation rather than new derivations or data.

major comments (2)

[Section introducing the Complex Brain Hypothesis (near the end of the abstract and corresponding discussion)] The manuscript asserts that coarse-grained inference yields high entropy yet low complexity (and thus low phenomenal content) in MPEs, but provides no equation, simulation, or explicit mapping from inference granularity to a concrete complexity measure such as Lempel-Ziv complexity, multiscale entropy, or integrated information. Without this link the central claim that complexity resolves the entropy-content conundrum remains qualitative and does not yet demonstrate why the same entropy elevation must produce divergent phenomenology.
[Discussion of human neuroimaging studies of MPEs induced by meditation and 5-MeO-DMT] The argument relies on prior neuroimaging findings of elevated entropy in MPEs; however, the distinction between fine- and coarse-grained regimes appears defined in terms of those same results rather than independent benchmarks. This risks circularity when the CBH is offered as a resolution of the EBH conundrum.

minor comments (2)

[Terminology throughout the CBH proposal] The terms 'grain of inference', 'fine-grained regime', and 'coarse-grained regime' would benefit from more precise operational definitions or references to existing formalisms in predictive-processing or active-inference literature.
[Paragraph contrasting phenomenology and perturbational signatures] Perturbational signatures that are said to diverge between the two regimes are mentioned but not illustrated with specific TMS-EEG or similar metrics; adding a brief table or figure summarizing expected signatures would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and insightful comments, which help clarify how the Complex Brain Hypothesis can be more rigorously presented. We address each major comment below, indicating planned revisions where appropriate.

read point-by-point responses

Referee: [Section introducing the Complex Brain Hypothesis (near the end of the abstract and corresponding discussion)] The manuscript asserts that coarse-grained inference yields high entropy yet low complexity (and thus low phenomenal content) in MPEs, but provides no equation, simulation, or explicit mapping from inference granularity to a concrete complexity measure such as Lempel-Ziv complexity, multiscale entropy, or integrated information. Without this link the central claim that complexity resolves the entropy-content conundrum remains qualitative and does not yet demonstrate why the same entropy elevation must produce divergent phenomenology.

Authors: We agree that the central claim of the CBH is currently presented at a conceptual level without explicit equations or simulations mapping inference granularity to specific complexity metrics. The manuscript's aim is to offer a theoretical reframing that distinguishes entropy from complexity via the grain of inference, drawing on existing predictive-processing ideas rather than deriving new quantitative models. In revision, we will add a dedicated subsection that sketches an explicit conceptual mapping: for example, relating coarse-grained inference to reduced multiscale entropy at finer temporal scales (while preserving overall entropy) and fine-grained inference to increased Lempel-Ziv complexity through amplified local fluctuations. This will include references to relevant computational literature and outline how future simulations could test the dissociation, thereby strengthening the link between inference grain and divergent phenomenology. revision: partial
Referee: [Discussion of human neuroimaging studies of MPEs induced by meditation and 5-MeO-DMT] The argument relies on prior neuroimaging findings of elevated entropy in MPEs; however, the distinction between fine- and coarse-grained regimes appears defined in terms of those same results rather than independent benchmarks. This risks circularity when the CBH is offered as a resolution of the EBH conundrum.

Authors: We acknowledge the risk of circularity and will revise the manuscript to clarify that the fine- versus coarse-grained regimes are defined independently from the neuroimaging data, drawing instead from the theoretical framework of hierarchical predictive processing in which inference grain refers to the spatial and temporal scale at which uncertainty is resolved (e.g., as formalized in active inference models). The MPE and HCPE findings are then interpreted as exemplars of these pre-defined regimes. To further mitigate circularity, the revised text will emphasize that the CBH generates testable predictions for new experiments using independent measures of inference grain, such as task-based paradigms or perturbational complexity indices, rather than relying solely on post-hoc reinterpretation of existing entropy results. revision: yes

Circularity Check

0 steps flagged

No significant circularity; CBH is a conceptual proposal building on but not reducing to EBH inputs

full rationale

The paper identifies a conundrum between EBH predictions and recent MPE neuroimaging data, then proposes CBH as a refinement in which complexity (modulated by inference grain) indexes phenomenal richness instead of entropy. No equations, fitted parameters, or self-citations are shown to make any central claim equivalent to its inputs by construction. The grain-of-inference distinction is presented as a qualitative regime argument rather than a tautological redefinition or statistical fit of the same data. The derivation remains self-contained as a hypothesis that can be tested against independent benchmarks outside the cited EBH framework.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The proposal rests on domain assumptions from prior neuroimaging studies and the Entropic Brain Hypothesis; no free parameters or new invented entities with independent evidence are introduced in the abstract.

axioms (2)

domain assumption Entropy of spontaneous brain activity marks phenomenal richness
Invoked as the basis of the Entropic Brain Hypothesis and the observed conundrum.
domain assumption MPEs induced by meditation and possibly 5-MeO-DMT exhibit increased neurophysiological entropy
Cited as the empirical observation creating the puzzle for the existing hypothesis.

invented entities (1)

Complex Brain Hypothesis no independent evidence
purpose: To index phenomenal richness by complexity rather than entropy via grain of inference
New conceptual framework introduced to resolve the conundrum.

pith-pipeline@v0.9.0 · 5829 in / 1298 out tokens · 61867 ms · 2026-05-19T18:30:01.655205+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

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ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

complexity ... equal to the entropy of those beliefs, relative to some prior beliefs ... KL divergence between posterior and prior beliefs

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Reference graph

Works this paper leans on

19 extracted references · 19 canonical work pages · 1 internal anchor

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entropic brain hypothesis

The Complex Brain Hypothesis: Resolving the Entropy-Content Conundrum in Minimal Phenomenal Experience Jonas Mago1+* , Edmundo Lopez-Sola2,3+, Jakub Vohryzek2,3+, Michael Lifshitz4,5, Robin Carhart-Harris6,7, Karl Friston8, Shamil Chandaria2 + Shared first authorship * Corresponding author: jonas.h.mago@gmail.com 1 Integrated Program in Neuroscience, McGi...

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For example, the principles of efficient encoding suggest that the variational and thermodynamic free energy share the same minima (Sengupta et al., 2013, 2016)

On this view, there is a close relationship between the entropy of brain activity and the entropy of beliefs encoded by brain activity that arises in several settings. For example, the principles of efficient encoding suggest that the variational and thermodynamic free energy share the same minima (Sengupta et al., 2013, 2016). Free energy corresponds to ...

work page 2013
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In terms of consciousness studies, the close relationship leads to a dual aspect (Markovian) monism, in which the variational and thermodynamic entropy rest upon the same dynamics

and the Jarzynski equality (Evans, 2003; Jarzynski, 1997). In terms of consciousness studies, the close relationship leads to a dual aspect (Markovian) monism, in which the variational and thermodynamic entropy rest upon the same dynamics

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Complexity on this view scores the divergence between posterior and prior beliefs (see figure 1)

Crucially, one can rearrange the constraints (i.e., expected energy) and entropy in free energy to express it as complexity minus accuracy (Penny, 2012). Complexity on this view scores the divergence between posterior and prior beliefs (see figure 1). In other words, it reflects the degrees of freedom used to provide an accurate account of the sensorium a...

work page 2012
[5]

The variational free energy F can be decomposed into a complexity term and an accuracy term

Free energy as a trade-off between complexity and accuracy. The variational free energy F can be decomposed into a complexity term and an accuracy term. Complexity corresponds to the Kullback–Leibler divergence between posterior and prior beliefs, 𝐷{"#}[𝑄(𝑥)||𝑃(𝑥)], and reflects the degree to which posterior beliefs must deviate from prior expectations to...

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In what follows, we now consider the distinction between entropy and complexity in light of various brain states and their measurement

that itself inherits from Kolmogorov complexity (Wallace & Dowe, 1999). In what follows, we now consider the distinction between entropy and complexity in light of various brain states and their measurement. Taken together, the considerations above motivate the following qualified inference: Shannon entropy is a measure of information content of a probabi...

work page 1999
[7]

The entropic brain hypothesis (EBH) implies a monotonic mapping from phenomenological content to entropy

The entropy–content conundrum. The entropic brain hypothesis (EBH) implies a monotonic mapping from phenomenological content to entropy. This would predict that minimal-content states are associated with low entropy while content-rich states are associated with high entropy. However, empirical evidence indicates that both MPEs (e.g., jhāna, 5-MeO-DMT) and...

work page 2021
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Mona Lisa

and is sourced from Wikimedia Commons (“Mona Lisa” with DeepDream effect using VGG16 network trained on ImageNet, 2024). These two inferential regimes can also be understood through the lens of algorithmic information theory (AIT). A central insight of AIT is that the best explanation of a dataset is the one that provides the greatest compression. This is...

work page 2024
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reality model

and variational inference generally (Hinton & Zemel, 1993). Technically, variational free energy is a tractable bound on total description length: where the negative description length L(D) is known as log model evidence or marginal likelihood in statistics, or an evidence lower bound (ELBO) in machine learning (Winn et al., 2005). It is important to note...

work page 1993
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Conceptual illustration of the relationship between model complexity (black), entropy (red), and phenomenal richness

Solving the conundrum: complexity, entropy and phenomenal richness. Conceptual illustration of the relationship between model complexity (black), entropy (red), and phenomenal richness. The left panels recapitulate the three regimes of inference in Figure 3 that inherit from reduced prior precision in the context of unattenuated and attenuated sensory (i....

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As black coffee and white cream mix, entropy increases monotonically, reflecting the growing number of particle configurations consistent with the systems state

Entropy and complexity in the coffee–cream mixing process (adapted from Aaronson et al., 2014). As black coffee and white cream mix, entropy increases monotonically, reflecting the growing number of particle configurations consistent with the systems state. At coarse-grained scales, however, complexity rises during the formation of structured swirls and t...

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Aaronson et al. (2014) model apparent complexity as the Kolmogorov complexity of a coarse-grained representation of the coffee (voxels of coffee color). Initially, the coarse-grained description is simple (white voxels above black voxels). In the intermediate regime, describing the intricate swirls requires many bits, yielding high apparent complexity. Fi...

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In short, complexity isolates the structural aspects of a system by filtering out randomness, i.e., it 15 captures the organized form rather than noise (Gell-Mann & Lloyd, 1996)

for a discussion in the context of generative models and machine learning. In short, complexity isolates the structural aspects of a system by filtering out randomness, i.e., it 15 captures the organized form rather than noise (Gell-Mann & Lloyd, 1996). Following our previous reasoning, higher apparent complexity is related to richer and more elaborate ex...

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The red curve depicts the entropy of posterior beliefs or their neuronal parameterization; it increases monotonically as prior constraints are relaxed

Entropy rises in both HCPEs and absorptive states, but complexity diverges depending on the inferential regime. The red curve depicts the entropy of posterior beliefs or their neuronal parameterization; it increases monotonically as prior constraints are relaxed. The purple curve represents complexity under fine-grained HCPE inference: unattenuated sensor...

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how rich

Three-dimensional extension of the entropic brain hypothesis. (a) A three-dimensional schematic showing how adding a third variable, here labeled wakefulness, separates states with low phenomenal richness and high entropy (MPE) or low entropy (sleep). When this surface is projected onto the two-dimensional plane, the pattern in panel (b) emerges. (b) 18 P...

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Quantifying the Rise and Fall of Complexity in Closed Systems: The Coffee Automaton

an underfitting, where there is a low-precision, coarse-grained regime characteristic of MPEs, in which a stable, low-dimensional model smooths away variability into content-minimal awareness. By embedding entropy within this broader information-theoretic and hierarchical framework, the CBH preserves the core insight of the EBH, while explaining why high ...

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25 Carhart-Harris, R. L., Muthukumaraswamy, S., Roseman, L., Kaelen, M., Droog, W., Murphy, K., Tagliazucchi, E., Schenberg, E. E., Nest, T., & Orban, C. (2016). Neural correlates of the LSD experience revealed by multimodal neuroimaging. Proceedings of the National Academy of Sciences, 113(17), 4853–4858. Carroll, S. (2017). The big picture: On the origi...

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[1] [1]

entropic brain hypothesis

The Complex Brain Hypothesis: Resolving the Entropy-Content Conundrum in Minimal Phenomenal Experience Jonas Mago1+* , Edmundo Lopez-Sola2,3+, Jakub Vohryzek2,3+, Michael Lifshitz4,5, Robin Carhart-Harris6,7, Karl Friston8, Shamil Chandaria2 + Shared first authorship * Corresponding author: jonas.h.mago@gmail.com 1 Integrated Program in Neuroscience, McGi...

work page 2022

[2] [2]

For example, the principles of efficient encoding suggest that the variational and thermodynamic free energy share the same minima (Sengupta et al., 2013, 2016)

On this view, there is a close relationship between the entropy of brain activity and the entropy of beliefs encoded by brain activity that arises in several settings. For example, the principles of efficient encoding suggest that the variational and thermodynamic free energy share the same minima (Sengupta et al., 2013, 2016). Free energy corresponds to ...

work page 2013

[3] [3]

In terms of consciousness studies, the close relationship leads to a dual aspect (Markovian) monism, in which the variational and thermodynamic entropy rest upon the same dynamics

and the Jarzynski equality (Evans, 2003; Jarzynski, 1997). In terms of consciousness studies, the close relationship leads to a dual aspect (Markovian) monism, in which the variational and thermodynamic entropy rest upon the same dynamics

work page 2003

[4] [4]

Complexity on this view scores the divergence between posterior and prior beliefs (see figure 1)

Crucially, one can rearrange the constraints (i.e., expected energy) and entropy in free energy to express it as complexity minus accuracy (Penny, 2012). Complexity on this view scores the divergence between posterior and prior beliefs (see figure 1). In other words, it reflects the degrees of freedom used to provide an accurate account of the sensorium a...

work page 2012

[5] [5]

The variational free energy F can be decomposed into a complexity term and an accuracy term

Free energy as a trade-off between complexity and accuracy. The variational free energy F can be decomposed into a complexity term and an accuracy term. Complexity corresponds to the Kullback–Leibler divergence between posterior and prior beliefs, 𝐷{"#}[𝑄(𝑥)||𝑃(𝑥)], and reflects the degree to which posterior beliefs must deviate from prior expectations to...

work page 1993

[6] [6]

In what follows, we now consider the distinction between entropy and complexity in light of various brain states and their measurement

that itself inherits from Kolmogorov complexity (Wallace & Dowe, 1999). In what follows, we now consider the distinction between entropy and complexity in light of various brain states and their measurement. Taken together, the considerations above motivate the following qualified inference: Shannon entropy is a measure of information content of a probabi...

work page 1999

[7] [7]

The entropic brain hypothesis (EBH) implies a monotonic mapping from phenomenological content to entropy

The entropy–content conundrum. The entropic brain hypothesis (EBH) implies a monotonic mapping from phenomenological content to entropy. This would predict that minimal-content states are associated with low entropy while content-rich states are associated with high entropy. However, empirical evidence indicates that both MPEs (e.g., jhāna, 5-MeO-DMT) and...

work page 2021

[8] [8]

Mona Lisa

and is sourced from Wikimedia Commons (“Mona Lisa” with DeepDream effect using VGG16 network trained on ImageNet, 2024). These two inferential regimes can also be understood through the lens of algorithmic information theory (AIT). A central insight of AIT is that the best explanation of a dataset is the one that provides the greatest compression. This is...

work page 2024

[9] [9]

reality model

and variational inference generally (Hinton & Zemel, 1993). Technically, variational free energy is a tractable bound on total description length: where the negative description length L(D) is known as log model evidence or marginal likelihood in statistics, or an evidence lower bound (ELBO) in machine learning (Winn et al., 2005). It is important to note...

work page 1993

[10] [10]

Conceptual illustration of the relationship between model complexity (black), entropy (red), and phenomenal richness

Solving the conundrum: complexity, entropy and phenomenal richness. Conceptual illustration of the relationship between model complexity (black), entropy (red), and phenomenal richness. The left panels recapitulate the three regimes of inference in Figure 3 that inherit from reduced prior precision in the context of unattenuated and attenuated sensory (i....

work page 2025

[11] [11]

As black coffee and white cream mix, entropy increases monotonically, reflecting the growing number of particle configurations consistent with the systems state

Entropy and complexity in the coffee–cream mixing process (adapted from Aaronson et al., 2014). As black coffee and white cream mix, entropy increases monotonically, reflecting the growing number of particle configurations consistent with the systems state. At coarse-grained scales, however, complexity rises during the formation of structured swirls and t...

work page 2014

[12] [12]

all brown voxels

Aaronson et al. (2014) model apparent complexity as the Kolmogorov complexity of a coarse-grained representation of the coffee (voxels of coffee color). Initially, the coarse-grained description is simple (white voxels above black voxels). In the intermediate regime, describing the intricate swirls requires many bits, yielding high apparent complexity. Fi...

work page 2014

[13] [13]

In short, complexity isolates the structural aspects of a system by filtering out randomness, i.e., it 15 captures the organized form rather than noise (Gell-Mann & Lloyd, 1996)

for a discussion in the context of generative models and machine learning. In short, complexity isolates the structural aspects of a system by filtering out randomness, i.e., it 15 captures the organized form rather than noise (Gell-Mann & Lloyd, 1996). Following our previous reasoning, higher apparent complexity is related to richer and more elaborate ex...

work page 1996

[14] [14]

The red curve depicts the entropy of posterior beliefs or their neuronal parameterization; it increases monotonically as prior constraints are relaxed

Entropy rises in both HCPEs and absorptive states, but complexity diverges depending on the inferential regime. The red curve depicts the entropy of posterior beliefs or their neuronal parameterization; it increases monotonically as prior constraints are relaxed. The purple curve represents complexity under fine-grained HCPE inference: unattenuated sensor...

work page 2005

[15] [15]

how rich

Three-dimensional extension of the entropic brain hypothesis. (a) A three-dimensional schematic showing how adding a third variable, here labeled wakefulness, separates states with low phenomenal richness and high entropy (MPE) or low entropy (sleep). When this surface is projected onto the two-dimensional plane, the pattern in panel (b) emerges. (b) 18 P...

work page 2009

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Quantifying the Rise and Fall of Complexity in Closed Systems: The Coffee Automaton

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