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Thermodynamics of consciousness: Non-equilibrium brain dynamics track conscious states.

Code ↔ Paper

8 matches between paragraphs of the paper and lines of its authors' code, computed by the harvester (lexical-v1). Click a colored paragraph or line to see its counterpart.

The 8 matches · 3 of them tie a paragraph to a whole file, not to given lines: weak matches, whose lines are not tinted
  1. [1] § STAR★Methods › Method details › Model optimization ↔ 1. Generative Effective Connectivity/Functions/linear_linfit_sub.m, lines 1–142 · score 0.81 · multivariate OU modeling, zero lag, lagged covariance, connectivity matrix, optimization, empirical
  2. [2] § STAR★Methods › Method details › Model optimization ↔ 1. Generative Effective Connectivity/GEC.m, lines 1–31 · score 0.76 · multivariate OU, zero lag, lagged covariance, connectivity matrix, empirical, fitting
  3. [3] § STAR★Methods › Method details › Model optimization ↔ 1. Generative Effective Connectivity/Functions/linear_linfit_sub.m, lines 1–142 · score 0.65 · multivariate OU model, lagged covariances, symmetric, optimization, noise, matrix
  4. [4] § STAR★Methods › Method details › Whole-brain modeling ↔ 2. Analytical Thermodynamics/Analytical_Thermo_NoneqMetrics.ipynb, lines 1–33 · score 0.60 · multivariate Ornstein Uhlenbeck, Wilson Cowan, linearization, dynamics, equilibrium, modeled
  5. [5] § STAR★Methods › Method details › Whole-brain modeling ↔ 3. FDT Violations/Functions/linear_sim_0init.m, the whole file · a weak match · score 0.59 · steady state, system dynamics, stochastic, linear, matrix, model
  6. [6] § STAR★Methods › Method details › Model optimization ↔ 1. Generative Effective Connectivity/Functions/linear_int.m, the whole file · a weak match · score 0.57 · functional connectivity, covariance matrix, Sylvester, Lyapunov, model
  7. [7] § Results ↔ 1. Generative Effective Connectivity/GEC.m, lines 1–31 · score 0.55 · zero lag, lagged covariance, multivariate, scores, empirical, EEG
  8. [8] § STAR★Methods › Method details › Whole-brain modeling ↔ 3. FDT Violations/Functions/linear_sim_0init.m, the whole file · a weak match · score 0.55 · Gaussian noise, connectivity matrix, covariance, brain, modeling

Paper

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The authors' code

MATLAB · 163 lines · 7.1 KB · MIT · 2 matches

  1. function [Ceffsub,FCemp,FCsim] = linear_linfit_sub(tsdata,NPARCELLS,TR,Tinf,sigma,maxC, varargin)
  2. % LINEAR_LINFIT_SUB Fit an effective connectivity matrix C using FC(0) and lagged covariance
  3. % for a single subject under a multivariate OU model.
  4. %
  5. % [Ceff, FCemp, FCsim] = LINEAR_LINFIT_SUB(tsdata, nParcels, TR, Tinf, sigma, maxC, ...)
  6. %
  7. % Inputs
  8. % tsdata : empirical time series.
  9. % nParcels : number of parcels (integer).
  10. % TR : sampling interval (seconds).
  11. % Tinf : integer number of samples to trim before FC/COV.
  12. % sigma : (scalar) noise variance for the OU model simulator.
  13. % maxC : (scalar) normalization applied to C.
  14. %
  15. % Name-Value pairs (optional)
  16. % 'Tau' : lag in samples for lagged covariance target (default = 1).
  17. % It can be modified depending on the data.
  18. % 'EpsFC' : learning rate for FC(0) term (default = 1e-4).
  19. % MODIFY DEPENDING ON THE FITTING LEVELS
  20. % 'EpsTau' : learning rate for lagged covariance term (default = 1e-4).
  21. % MODIFY DEPENDING ON THE FITTING LEVELS
  22. % 'ErrorTol' : stop when (old - new)/new < ErrorTol (default = 1e-5).
  23. % Increase as possible...
  24. % 'MaxIter' : maximum number of iterations (default = 5000).
  25. % 'UseAbsCov' : use abs(cov) (true) to stabilize the variance normalization (default = true).
  26. %
  27. % Outputs
  28. % Ceff : [nParcels x nParcels] fitted effective connectivity matrix.
  29. % FCemp : [nParcels x nParcels] empirical FC(0) (Pearson correlation).
  30. % FCsim : [nParcels x nParcels] simulated FC(0) from final model.
  31. %
  32. % Notes
  33. %
  34. % • The update keeps C non-negative and re-enforces diagonal dominance to
  35. % satisfy a Hurwitz-like stability criterion at each step.
  37. % Author : Tomas Berjaga Buisan
  39. % Copyright
  40. % © 2025 Your Lab. MIT License.
  41. % ========================================================================
  43. % ──────────────────────────────────────────────────────────────────────────
  44. % Parse & validate inputs
  45. % ──────────────────────────────────────────────────────────────────────────
  46. p = inputParser;
  47. p.addParameter('Tau', 1, @(x)isnumeric(x)&&isscalar(x)&&x>=0);
  48. p.addParameter('EpsFC', 4e-4, @(x)isnumeric(x)&&isscalar(x)&&x>0);
  49. p.addParameter('EpsTau', 1e-4, @(x)isnumeric(x)&&isscalar(x)&&x>0);
  50. p.addParameter('ErrorTol', 1e-5, @(x)isnumeric(x)&&isscalar(x)&&x>0);
  51. p.addParameter('MaxIter', 5000, @(x)isnumeric(x)&&isscalar(x)&&x>0);
  52. p.addParameter('Seed', [], @(x)isempty(x)||(isnumeric(x)&&isscalar(x)));
  53. p.addParameter('UseAbsCov', true, @(x)islogical(x)&&isscalar(x));
  54. p.parse(varargin{:});
  56. Tau = p.Results.Tau;
  57. epsFC = p.Results.EpsFC;
  58. epsTau = p.Results.EpsTau;
  59. errTol = p.Results.ErrorTol;
  60. maxIter = p.Results.MaxIter;
  61. seed = p.Results.Seed;
  62. useAbs = p.Results.UseAbsCov;
  64. % ──────────────────────────────────────────────────────────────────────────
  65. % Empirical targets: FC(0) and normalized lagged covariance COV_tau
  66. % ──────────────────────────────────────────────────────────────────────────
  68. indexN = 1:NPARCELLS;
  69. N = length(indexN);
  70. ts2 = tsdata(indexN,Tinf:end-Tinf); % trim edges
  72. % Empirical zero-lag FC (Pearson)
  73. FCemp = corrcoef(ts2');
  74. % Empirical covariance for variance normalization
  75. COVemp = cov(ts2');
  77. if useAbs
  78. COVemp = abs(COVemp);
  79. FCemp = abs(FCemp);
  80. end
  82. % Lagged covariance at lag = Tau samples (normalized)
  83. COVtauEmp = zeros(N, N);
  84. tst = ts2';
  86. for i = 1:N
  87. for j = 1:N
  88. sigratio(i,j) = 1/sqrt(COVemp(i,i))/sqrt(COVemp(j,j));
  89. [clag, lags] = xcov(tst(:,i),tst(:,j),Tau);
  90. indx = find(lags == Tau);
  91. COVtauemp(i,j) = clag(indx)/size(tst,1);
  92. end
  93. end
  95. COVtauemp = COVtauemp.*sigratio;
  97. % ──────────────────────────────────────────────────────────────────────────
  98. % Initialize connectivity C (nonnegative, symmetric, diagonally dominant)
  99. % ──────────────────────────────────────────────────────────────────────────
  101. C = abs(randn(N)); % random nonnegative weights
  102. C = (C + C.')/2; % symmetrize
  103. diagonal = sum(abs(C),2) - abs(diag(C));
  104. C = diag(diagonal+eps) + C.*~eye(N); % enforce diagonal dominance (Hurwitz-like)
  105. %C = C + 0.1 * randn(NPARCELLS); % Add random asymmetry (OPTIONAL)
  106. C = C/max(max(C))*maxC; % normalize to maxC
  108. % ──────────────────────────────────────────────────────────────────────────
  109. % Optimize C by matching FC(0) and normalized COV(Tau)
  110. % ──────────────────────────────────────────────────────────────────────────
  112. Cnew = C;
  113. olderror = inf;
  115. for iter = 1:maxIter
  116. % --- Simulate OU / linear model ---
  117. [FCsim, COVsim, A] = linear_int(Cnew, sigma);
  119. % Compute normalized lagged covariance from model
  120. COVtausim = expm((Tau*TR)*A)*COVsim;
  121. COVtausim = COVtausim(1:N,1:N);
  122. for i = 1:N
  123. for j = 1:N
  124. sigratiosim(i,j) = 1/sqrt(COVsim(i,i))/sqrt(COVsim(j,j));
  125. end
  126. end
  127. COVtausim = COVtausim.*sigratiosim;
  130. % Stopping criterion (checked every 10 iters)
  131. if mod(iter,10) < 0.1
  132. errornow = mean(mean((FCemp - FCsim).^2)) + mean(mean((COVtauemp - COVtausim).^2));
  133. if (olderror - errornow)/errornow < errTol
  134. % disp('---> (olderror - errornow)/errornow < error_tol')
  135. break;
  136. end
  137. if olderror < errornow
  138. % disp('---> olderror < errornow')
  139. break;
  140. end
  141. olderror = errornow;
  142. end
  144. %%% Learning - Gradient-like update
  145. for i = 1:N
  146. for j = 1:N
  147. if (Cnew(i,j) > 0 || j == N-i+1)
  148. Cnew(i,j) = Cnew(i,j) + epsFC*(FCemp(i,j) - FCsim(i,j)) ...
  149. + epsTau*(COVtauemp(i,j) - COVtausim(i,j));
  150. if Cnew(i,j) < 0
  151. Cnew(i,j) = 0;
  152. end
  153. end
  154. end
  155. end
  157. % Re-enforce diagonal dominance (Hurwitz-like) and renormalize
  158. diagonal = sum(abs(Cnew), 2) - abs(diag(Cnew));
  159. Cnew = diag(diagonal+eps) + Cnew.*~eye(N); % enforce diagonal dominance (Hurwitz-like)
  160. Cnew = Cnew/max(max(Cnew))*maxC;
  161. end
  162. Ceffsub = Cnew;
  163. end

linear_linfit_sub.m at commit 7d60464, under MIT · at the source

Overview

Authors: Tomas Berjaga-Buisan1, Juan Manuel Monti2,3, Martina Cortada4,5, Michele A Colombo6, Sebastian M Geli1, Gianluca Gaglioti6, Simone Sarasso6, Morten L Kringelbach7,8,9,10, Maurizio Corbetta11,12,13, Maria V Sanchez-Vives4,14, Marcello Massimini6,15, Yonatan Sanz Perl10,16,17, Gustavo Deco10,14,17
ORCID iDs: Tomas Berjaga-Buisan, Simone Sarasso, Marcello Massimini
17 affiliations
  1. Center for Brain and Cognition, Computational Neuroscience Group, Department of Engineering, Universitat Pompeu Fabra, 08005 Barcelona, Spain
  2. Instituto de Física Rosario CONICET-UNR, Rosario 2000, Argentina
  3. Laboratorio de Colisiones Atómicas, FCEIA, Universidad Nacional de Rosario, Rosario 2000, Argentina
  4. Institut d’Investigacions Biomèdiques August Pi i Sunyer (IDIBAPS), 08036 Barcelona, Spain
  5. Facultat de Física, Universitat de Barcelona (UB), 08028 Barcelona, Spain
  6. Department of Biomedical and Clinical Sciences, Università degli Studi di Milano, 20157 Milan, Italy
  7. Centre for Eudaimonia and Human Flourishing, Linacre College, University of Oxford, Oxford OX3 9BX, UK
  8. Department of Psychiatry, University of Oxford, Oxford OX3 7JX, UK
  9. Center for Music in the Brain, Department of Clinical Medicine, Aarhus University, 8000 Aarhus C, Denmark
  10. International Centre for Flourishing, Universities of Oxford (UK), Aarhus (Denmark) and Pompeu Fabra (Spain), Oxford OX3 9BX, UK
  11. Padova Neuroscience Center (PNC), University of Padova, 35129 Padova, Italy
  12. Department of Neuroscience, University of Padova, 35128 Padova, Italy
  13. Venetian Institute of Molecular Medicine (VIMM), 35129 Padova, Italy
  14. Institució Catalana de Recerca i Estudis Avançats (ICREA), 08010 Barcelona, Spain
  15. IRCCS, Fondazione Don Carlo Gnocchi Onlus, 20148 Milan, Italy
  16. Department of Engineering, Universidad de San Andrés, Buenos Aires B1644BID, Argentina
  17. Center for Brain and Cognition, Computational Neuroscience Group, Faculty of Medicine and Life Sciences, Universitat Pompeu Fabra, 08005 Barcelona, Spain
Institutions: Universitat Pompeu Fabra (Spain); Consejo Nacional de Investigaciones Científicas y Técnicas (Argentina); National University of Rosario (Argentina); Institute of Physics Rosario (Argentina); Consorci Institut D'Investigacions Biomediques August Pi I Sunyer (Spain); Universitat de Barcelona (Spain); University of Milan (Italy); Aarhus University (Denmark); University of Oxford (United Kingdom); University of Padua (Italy); Veneto Institute of Molecular Medicine (Italy); Institució Catalana de Recerca i Estudis Avançats (Spain); Don Carlo Gnocchi Foundation (Italy); University of San Andrés (Argentina)
Journal: Cell reports, volume 45, issue 8, article 117782
Dates: received 3 December 2025; accepted 15 July 2026; published online 31 July 2026; in print July 2026
Type: Research article · Language: English
License: CC BY
Identifiers: DOI 10.1016/j.celrep.2026.117782 · PMID 42541725 · PMCID PMC13506674 · OpenAlex W7171968608
Open access: gold, a free copy (OpenAlex)
Status: code verified
Categories: EEG (modality), extracellular electrophysiology (units, LFP) (modality), other condition (population), cognitive (subfield)
Methods: Spectral & time-frequency, Preprocessing, Connectivity, Statistics, Smoothing, state filtering, decompositions, Machine learning, Complexity
Keywords: consciousness, disorders of consciousness, anesthesia, perturbational complexity index, whole-brain modeling, non-equilibrium, thermodynamics, fluctuation-dissipation theorem, EEG, LFP
Topic: Neural dynamics and brain function (Cognitive Neuroscience, Neuroscience), according to OpenAlex
Funding: Agencia Estatal de Investigación; CONICET; Horizon 2020; AGAUR; European Research Council; ERDF; Fondazione Cassa di Risparmio di Padova e Rovigo
Citations: cited by 1 paper (Europe PMC); 100 references in the paper
Research resources: MATLAB RRID:SCR_001622, Python RRID:SCR_008394

Abstract

The quest for reliable and objective measures of consciousness is critical in basic and clinical neuroscience. Across species, the perturbational complexity index (PCI) has emerged as a robust empirical marker by directly perturbing the brain, yet its relationship to broader physical principles remains unclear. Here, we address this gap by introducing a non-invasive framework based on generative whole-brain models of non-equilibrium brain dynamics. Using these models, we identify violations of the fluctuation-dissipation theorem (FDT) in humans and rodents across wakefulness, anesthesia, and disorders of consciousness (DoC). Mirroring PCI, FDT violations decrease in unresponsive DoC and anesthesia compared with conscious conditions. These findings reveal a robust empirical link between PCI and non-equilibrium dynamics in spontaneous brain signals, suggesting that non-equilibrium dynamics capture an important aspect of perturbational complexity. Overall, this framework opens non-invasive, model-based avenues for understanding consciousness and supports efforts to assess its loss and recovery in health and disease.

Reproduced under the paper's license (CC BY), from the paper cited above.

Repositories

Its files are read in the Code ↔ Paper reader above, with 8 matches between paragraphs and lines of code.

Zenodo 20719663

License: MIT
State: the link answers, verified on 27 September 2026
Evidence: files inventoried
Size: 1 file
Software Heritage: not checked
Found in: “Data and code availability”
Not found: README, license file, CITATION.cff, environment file, tests, continuous integration, documentation
Tools: Signal Processing Toolbox (2 files), Statistics and Machine Learning Toolbox (2 files), Matplotlib (1 file), NumPy (1 file), pandas (1 file), SciPy (1 file), statsmodels (1 file)
Availability: 1 check, the latest on 27 September 2026: the link answers (HTTP 200)
  • 27 September 2026: the link answers (HTTP 200)
14 files
At the source: doi.org/10.5281/zenodo.20719663

tomasberjagabuisan/Thermo-Consciousness

License: MIT
State: the link answers, verified on 27 September 2026
Evidence: files inventoried
Commit: 7d604646ae36fab50829437977a037abce5963f3, 19 August 2026
Languages: MATLAB (11), Jupyter (1)
Size: 14 files, 12 scripts
Software Heritage: not archived
Found in: “Data and code availability”
Holds: README, license file, 1 notebook
Not found: CITATION.cff, environment file, tests, continuous integration, documentation
Tools: Signal Processing Toolbox (2 files), Statistics and Machine Learning Toolbox (2 files), Matplotlib (1 file), NumPy (1 file), pandas (1 file), SciPy (1 file), statsmodels (1 file)
Availability: 1 check, the latest on 27 September 2026: the link answers
  • 27 September 2026: the link answers
14 files
At the source: github.com/tomasberjagabuisan/Thermo-Consciousness

The paper's code and data availability statement is in the Data section.

Tracing map

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  • 2 repositories of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
  • 24 scripts, each with its path and the digest of its content;
  • 8 matches between paragraphs of the paper and lines of the code (method lexical-v1);
  • neither the text of the paper nor the code itself.

Its JSON (tracing-map.json) is deposited on Zenodo with its DOI once the map is validated.

Data

Datasets cited

Data and code availability

Raw LFP recordings from eight adult male C57BL/6J mice across different anesthesia levels are publicly available at the EBRAINS repository (https://doi.org/10.25493/WKA8-Q4T).

The human anesthesia EEG dataset analyzed in this study was not generated specifically for the present study. It was originally collected in the context of the EU Horizon 2020 LUMINOUS project (grant no. 686764) and deposited by the original investigators on Zenodo (https://doi.org/10.5281/zenodo.806176), where it is indexed in the EU Open Research Repository. The repository record and metadata are publicly accessible, while the underlying human participant-level EEG data are available under restricted access due to ethical restrictions associated with the original data collection. Access requests may be submitted through Zenodo and are assessed by the relevant data custodians.

All original code used for data analysis, modeling of spontaneous fluctuations, fitting of generative effective connectivity, computation of FDT violations, and calculation of complementary thermodynamic metrics has been deposited at Zenodo and is publicly available at https://doi.org/10.5281/zenodo.20719663. The code is also available in the associated GitHub repository: https://github.com/tomasberjagabuisan/Thermo-Consciousness

Additional data, including raw EEG signals from patients with DoC, along with associated metadata, are available from the authors upon reasonable request and subject to a data sharing agreement.

Reproduced under the paper's license (CC BY), from the paper cited above.

Versions

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Version 2, 28 September 2026

  • Publisher: n/a → Cell Press

Version 1, 27 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 13 authors, 10 keywords, 7 funders, 100 references, 2 RRIDs.

Cite

This paper

Berjaga-Buisan, T., Monti, J. M., Cortada, M., Colombo, M. A., Geli, S. M., Gaglioti, G., Sarasso, S., Kringelbach, M. L., Corbetta, M., Sanchez-Vives, M. V., Massimini, M., Perl, Y. S., & Deco, G. (2026). Thermodynamics of consciousness: Non-equilibrium brain dynamics track conscious states. Cell reports, 45(8), 117782. https://doi.org/10.1016/j.celrep.2026.117782

BibTeX

@article{berjagabuisan2026thermodynamics,
author = {Berjaga-Buisan, Tomas and Monti, Juan Manuel and Cortada, Martina and Colombo, Michele A and Geli, Sebastian M and Gaglioti, Gianluca and Sarasso, Simone and Kringelbach, Morten L and Corbetta, Maurizio and Sanchez-Vives, Maria V and Massimini, Marcello and Perl, Yonatan Sanz and Deco, Gustavo},
title = {{Thermodynamics of consciousness: Non-equilibrium brain dynamics track conscious states}},
journal = {Cell reports},
year = {2026},
month = jul,
volume = {45},
number = {8},
pages = {117782},
publisher = {Cell Press},
issn = {2211-1247},
doi = {10.1016/j.celrep.2026.117782},
url = {https://doi.org/10.1016/j.celrep.2026.117782},
pmid = {42541725},
pmcid = {PMC13506674}
}

RIS

TY - JOUR
AU - Berjaga-Buisan, Tomas
AU - Monti, Juan Manuel
AU - Cortada, Martina
AU - Colombo, Michele A
AU - Geli, Sebastian M
AU - Gaglioti, Gianluca
AU - Sarasso, Simone
AU - Kringelbach, Morten L
AU - Corbetta, Maurizio
AU - Sanchez-Vives, Maria V
AU - Massimini, Marcello
AU - Perl, Yonatan Sanz
AU - Deco, Gustavo
TI - Thermodynamics of consciousness: Non-equilibrium brain dynamics track conscious states
T2 - Cell reports
J2 - Cell Rep
PY - 2026
DA - 2026/07/31
VL - 45
IS - 8
SP - 117782
SN - 2211-1247
PB - Cell Press
DO - 10.1016/j.celrep.2026.117782
UR - https://doi.org/10.1016/j.celrep.2026.117782
LA - en
ER -

CSL-JSON

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