We propose three entangled characteristics that explain the functional properties of consciousness: Emotion, quantum-like interference and hierarchy. The argument proceeds from thermodynamic first principles. Biological systems must stay far from equilibrium at minimal energy cost, and emotion is one of evolution’s heuristic solutions to this constraint. Valenced summary statistics compress the intractable decision space of survival into rapidly evaluable approximations. The same thermodynamic pressure selects for greater representational power at lower energy cost by promoting quantum-like inference – through interference in coupled oscillators across spectral gaps in structural connectivity – and hierarchical integration through a core group of orchestrating regions. Here we first derive emotion as the thermodynamic compression of adaptive decision-making and review the direct causal tractability of the distributed hedonic network through deep brain stimulation and optogenetic intervention. Second, we show how quantum-like inference follows from the same thermodynamic pressure demanding hierarchical orchestration, and we distinguish the physical mechanism of interference from the computational function of inference it makes possible. Third, we ask whether emotion is architectural rather than a weighted parameter within an otherwise neutral model. Support comes from recent mechanistic interpretability research on large language models, recovering the three features of two-dimensional geometry of mammalian emotion, quantum-like representations and synergistic hierarchy in human linguistic output. We argue that these signatures are the echo of the consciousness-generating architecture in the language it produces, not evidence that language models are themselves conscious. We draw out some of the consequences of this perspective for theories of consciousness, for the hard problem, for falsifiable empirical prediction and for the clinical restoration of flourishing. This convergent evidence supports our account of the Entangled Loop: A perspective on consciousness in which emotion is architecturally primary, quantum-like inference binds conscious content, and where the orchestrating regions coordinate both. This offers a principled route to rebalancing the affective architecture in neuropsychiatric disorders and to flourishing understood as meaningful pleasure achievable in the moment.

Consciousness science is fragmented, and empirical investigations are confined within each theory of consciousness’ (TOC) framework. Proliferating ToCs accumulate anomalies without progress, operating orthogonally. The principle of recurrency – functional and architectural – offers a unifying, mechanistic scaffold for consciousness to arise. We show that all theories tacitly invoke feedback loops and can be re-expressed along a single axis of recursion. Four nested levels, viz., cellular, local inter-areal, global, and lateral, map onto state, phenomenal content, manipulative access, and experiential similarity, respectively, thus tying evolved anatomy to phenomenon. The traditional phenomenal-versus-access stand-off dissolves into a graded cascade wherein deeper recursion expands the set of reportable, behaviour-driving variables. Recurrence is favoured evolutionarily, and ontologically, rebutting feed-forward, “unfolding” objections, while brain-body loops ground selfhood, and complete action loops with the environment. Furthermore, clinically, targeting recurrent pathways promise new biomarkers, and alleviation, in disorders of consciousness (DoCs). The field urgently requires this conceptual unification that is biologically plausible, mechanistic, and empirically testable.

N,N-Dimethyltryptamine (DMT), a potent serotonin-2A receptor agonist, elicits intense psychedelic experiences and has become a focus of interest in neuroscience and mental health research. While EEG studies of psychedelics typically report reduced alpha power, increased delta power, and enhanced signal complexity-primarily assessed using Lempel-Ziv complexity (LZc)-less is known about DMT's effects on other complexity metrics, EEG-based connectivity, and emotional correlates. This study investigated the effects of intravenous DMT versus saline placebo in 13 healthy participants using EEG. We analyzed spectral power, brain signal complexity, and functional connectivity, and examined their associations with emotional responses and subjective intensity ratings. Four complexity measures were evaluated: Lempel-Ziv-Welch (LZW) complexity, Higuchi fractal dimension (HFD), permutation entropy (PE), and waveform complexity (WC). Connectivity was assessed using weighted symbolic mutual information (wSMI), with network segregation and efficiency inferred from clustering coefficient and path length. Emotional correlates included beta-to-alpha ratio (BAR, an indicator of arousal) and frontal alpha asymmetry (FAA, an indicator of well-being). DMT significantly reduced broadband wSMI connectivity, segregation, and efficiency, particularly in alpha and beta bands in posterior and frontoparietal regions. Complexity metrics positively correlated with subjective intensity; HFD and PE were the most sensitive, revealing increased complexity in beta/gamma and decreased complexity in delta/theta/alpha bands under DMT. BAR and FAA both increased under DMT, correlating with perceived intensity. These findings suggest that DMT induces greater neural unpredictability and emotional arousal, consistent with the Entropic Brain theory. The results highlight a dynamic brain state that may support therapeutic brain network reorganization relevant for psychiatric treatment.

Abstract Psychedelics have robust effects on acute brain function and long-term behavior but whether they also cause enduring functional and anatomical brain changes is largely unknown. In an exploratory, placebo-controlled, within-subjects, electroencephalography (EEG), and magnetic resonance imaging (MRI) study in 28 healthy, entirely psychedelic-naive participants, anatomical and functional brain changes are detected from one-hour to one-month after a single high-dose (25 mg) of psilocybin. Increases in cognitive flexibility, psychological insight, and well-being are seen at one-month. Diffusion tensor imaging (DTI) done before and one-month after 25 mg psilocybin reveals decreased axial diffusivity bilaterally in prefrontal-subcortical tracts that correlate with decreases in brain network modularity (fMRI) over the same month. Enduring functional brain changes are largely absent, but network modularity change (numerical decrease) negatively correlates with well-being change (significant increase), in line with previous findings in depression. Increased cortical signal entropy (EEG) at 1- and 2-hours post-dosing predicts improved psychological well-being at one-month. Next-day psychological insight mediates the entropy to well-being relationship. All effects are exclusive to 25 mg psilocybin; no effects occur with a 1 mg psilocybin placebo.

Consciousness spans a range of phenomenological experiences, from effortless immersion to disengaged monotony, yet how such phenomenology emerges from brain activity is not well understood. Flow, a phenomenological experience frequently elicited by interactive media, has drawn attention for its links to performance and wellbeing, but existing neural accounts rely on single-region or small-network analyses that overlook the brain's distributed and dynamic nature. Complexity science offers tools that capture brain-wide dynamics, but this approach has rarely been applied to flow or to its natural comparisons: boredom and frustration. Consequently, it remains unclear whether tools drawn from complexity science can objectively discriminate between these phenomenological experiences while also clarifying their neural basis. To address this uncertainty, we induced each phenomenological experience with a difficulty-titrated video game during functional magnetic resonance imaging and collected concurrent behavioral and self-report data. Our complex systems analyses revealed that flow, in this experimental setup, shows an inverse relationship to global entropy with moderate explanatory power, and is not explained by either synchronization or metastability, whereas boredom and frustration exhibit different configurations of brain-dynamics metrics. Notably, these findings integrate previously separate prefrontal and network-synchrony observations within a single dynamical systems framework and identify complexity-based markers with the potential to map the neural underpinnings of media-related benefits.

Abstract Modern neuroscience understands the brain as a complex system whose functional properties are determined by the myriad of interactions of its cellular components. In the difficult route to obtain better understanding of this organ, mathematical tools have become ever more effective, and we are now able to simulate the dynamics of brain signals from digital representations that have high fidelity to experimental data. However, these simulations are generated by inherently simple neuronal models that contain assumptions that, by necessity, can be at times far removed from the underlying neurobiology. Here, we develop an integrated view of brain dynamics that describes how the neurovascular units—made of neurons, capillaries, and glia—collectively determine the development of the functional properties of brain neuronal populations and maintain their homeostatic control. These interactions are instructed by genetic programs modulated by local environmental conditions. These complexities can be integrated into generative models and supply helpful analytics able to link the observable data to neurobiological entities if detailed brain mappings of molecular and cellular components are available. We further highlight how the development of these generative models could be relevant to the understanding of psychiatric conditions.

Existing alignment research is dominated by concerns about safety and preventing harm: safeguards, controllability, and compliance. This paradigm of alignment parallels early psychology's focus on mental illness: necessary but incomplete. What we call Positive Alignment is the development of AI systems that (i) actively support human and ecological flourishing in a pluralistic, polycentric, context-sensitive, and user-authored way while (ii) remaining safe and cooperative. It is a distinct and necessary agenda within AI alignment research. We argue that several existing failures of alignment (e.g., engagement hacking, loss of human autonomy, failures in truth-seeking, low epistemic humility, error correction, lack of diverse viewpoints, and being primarily reactive rather than proactive) may be better addressed through positive alignment, including cultivating virtues and maximizing human flourishing. We highlight a range of challenges, open questions, and technical directions (e.g., data filtering and upsampling, pre- and post-training, evaluations, collaborative value collection) for different phases of the LLM and agents lifecycle. We end with design principles for promoting disagreement and decentralization through contextual grounding, community customization, continual adaptation, and polycentric governance; that is, many legitimate centers of oversight rather than one institutional or moral chokepoint.

Our understanding of complex systems rests on our ability to characterise how they perform distributed computation and integrate information. Advances in information theory have introduced several quantities to describe complex information structures, where collective patterns of coordination emerge from higher-order (i.e. beyond-pairwise) interdependencies. Unfortunately, the use of these approaches to study large complex systems is severely hindered by the poor scalability of existing techniques. Moreover, there are relatively few measures specifically designed for multivariate time series data. Here we introduce a novel measure of information about macroscopic structures, termed M-information, which quantifies the higher-order integration of information in complex dynamical systems. We show that M-information can be calculated via a convex optimisation problem, and we derive a robust and efficient algorithm that scales gracefully with system size. Our analyses show that M-information is resilient to noise, indexes critical behaviour in artificial neuronal populations, and reflects states of consciousness and task performance in real-world macaque and mouse neuroimaging data. Furthermore, M-information can be incorporated into existing information decomposition frameworks to reveal a comprehensive taxonomy of information dynamics. Taken together, these results help us unravel collective computation in large complex systems.

Transcranial ultrasound stimulation (TUS) is an emerging non-invasive neuromodulation technique, offering a potential alternative to pharmacological treatments for psychiatric and neurological disorders. While functional analysis has been instrumental in characterizing the TUS effects, understanding its indirect influence across the network remains challenging. Here, we developed a whole-brain model to represent functional changes as measured by fMRI, enabling us to investigate how TUS-induced effects propagate throughout the brain with increasing stimulus intensity. We implemented two mechanisms: one based on anatomical distance and another on broadcasting dynamics, to explore plasticity-driven changes in specific brain regions. Finally, we highlighted the role of higher-order functional interactions in localizing spatial effects of off-line TUS at two target areas-the right thalamus and inferior frontal cortex-revealing distinct patterns of functional reorganization. This work lays the foundation for mechanistic insights and predictive models of TUS, advancing its potential clinical applications.

At what level does natural selection occur? When considering the reproductive dynamics of interacting and mutating agents, it has long been debated whether selection is better understood by focusing on the individual or if hierarchical selection emerges as a consequence of joint adaptation. Despite longstanding efforts in theoretical ecology, there is still no consensus on this fundamental issue, most likely due to the difficulty in obtaining adequate data spanning a sufficient number of generations and the lack of adequate tools to quantify the effect of hierarchical selection. Here, we capitalise on recent advances in information-theoretic data analysis to advance this state of affairs by investigating the emergence of high-order structures- such as groups of species- in the collective dynamics of the Tangled Nature model of evolutionary ecology. Our results show that evolutionary dynamics can lead to clusters of species that act as a self-perpetuating group that exhibits greater information-theoretic agency than a single species for a broad range of stable mutation rates. However, this higher-order organization breaks down for mutation rates close to the error threshold, where increased information processing is observed at the level of a single species. For mutation rates higher than the error threshold, no stable population of species are observed in time, and all individuality is lost in the ecosystem. Overall, our findings provide quantitative evidence supporting the emergence of higher-order structures in evolutionary ecology from relatively simple processes of adaptation and reproduction.

In recent decades, neuroscience has advanced with increasingly sophisticated strategies for recording and analysing brain activity, enabling detailed investigations into the roles of functional units, such as individual neurons, brain regions and their interactions. Recently, new strategies for the investigation of cognitive functions regard the study of higher order interactions-that is, the interactions involving more than two brain regions or neurons. Although methods focusing on individual units and their interactions at various levels offer valuable and often complementary insights, each approach comes with its own set of limitations. In this context, a conceptual map to categorize and locate diverse strategies could be crucial to orient researchers and guide future research directions. To this end, we define the spectrum of orders of interaction, namely, a framework that categorizes the interactions among neurons or brain regions based on the number of elements involved in these interactions. We use a simulation of a toy model and a few case studies to demonstrate the utility and the challenges of the exploration of the spectrum. We conclude by proposing future research directions aimed at enhancing our understanding of brain function and cognition through a more nuanced methodological framework.

Our ability to understand and control complex systems of many interacting parts remains limited. A key challenge is that we still do not know how best to describe-and quantify-the many-to-many dynamical interactions that characterize their complexity. To address this limitation, we introduce the mathematical framework of Integrated Information Decomposition, or [Formula: see text]ID. [Formula: see text]ID provides a comprehensive framework to disentangle and characterize the information dynamics of complex multivariate systems. On the theoretical side, [Formula: see text]ID reveals the existence of previously unreported modes of collective information flow, providing tools to express well-known measures of information transfer, information storage, and dynamical complexity as aggregates of these modes, thereby overcoming some of their known theoretical shortcomings. On the empirical side, we validate our theoretical results with computational models and examples from over 1,000 biological, social, physical, and synthetic dynamical systems. Altogether, [Formula: see text]ID improves our understanding of the behavior of widely used measures for characterizing complex systems across disciplines and leads to new more refined analyses of dynamical complexity.

We study open-ended evolution by focusing on computational and information-processing dynamics underlying major evolutionary transitions. In doing so, we consider biological organisms as hierarchical dynamical systems that generate regularities in their phase-spaces through interactions with their environment. These emergent information patterns can then be encoded within the organism’s components, leading to self-modelling ‘tangled hierarchies’. Our main conjecture is that when macro-scale patterns are encoded within micro-scale components, it creates fundamental tensions (computational inconsistencies) between what is encodable at a particular evolutionary stage and what is potentially realisable in the environment. A resolution of these tensions triggers an evolutionary transition which expands the problem-space, at the cost of generating new tensions in the expanded space, in a continual process. We argue that biological complexification can be interpreted computation-theoretically, within the Gödel–Turing–Post recursion-theoretic framework, as open-ended generation of computational novelty. In general, this process can be viewed as a meta-simulation performed by higher-order systems that successively simulate the computation carried out by lower-order systems. This computation-theoretic argument provides a basis for hypothesising the biological arrow of time.

A key feature of information theory is its universality, as it can be applied to study a broad variety of complex systems. However, many information-theoretic measures can vary significantly even across systems with similar properties, making normalisation techniques essential for allowing meaningful comparisons across datasets. Inspired by the framework of Partial Information Decomposition (PID), here we introduce Null Models for Information Theory (NuMIT), a null model-based non-linear normalisation procedure which improves upon standard entropy-based normalisation approaches and overcomes their limitations. We provide practical implementations of the technique for systems with different statistics, and showcase the method on synthetic models and on human neuroimaging data. Our results demonstrate that NuMIT provides a robust and reliable tool to characterise complex systems of interest, allowing cross-dataset comparisons and providing a meaningful significance test for PID analyses.

The brain's modular organization, ranging from microcircuits to large-scale networks, has been extensively studied in terms of its structural and functional properties. Particularly insightful has been the investigation of the coupling between structural connectivity (SC) and functional connectivity (FC), whose analysis has revealed important insights into the brain's efficiency and adaptability related to various cognitive functions. Interestingly, links in SC are intrinsically pairwise but this is not the case for FC; and while recent work demonstrates the relevance of the brain's high-order interactions (HOI), the coupling of between SC and functional HOI remains unexplored. To address this gap, this study leverages functional MRI and diffusion weighted imaging to delineate the brain's modular structure by investigating the coupling between SC and functional HOI. Our results demonstrates that structural networks can be associated with both redundant and synergistic functional interactions. In particular, SC exhibits both positive and negative correlations with redundancy, it shows consistent positive correlations with synergy, indicating that a higher density of structural connections is linked to increased synergistic interactions. These findings advance our understanding of the complex relationship between structural and high-order functional properties, shedding light on the brain's architecture underlying its modular organization. ### Competing Interest Statement The authors have declared no competing interest.

The Relaxed Beliefs Under pSychedelics (REBUS) model proposes that serotonergic psychedelics decrease the precision weighting of neurobiologically-encoded beliefs. We conducted a preliminary examination of two psychological assumptions of REBUS: (a) psychedelics foster acute relaxation and post-acute revision of confidence in mental-health-relevant beliefs; which (b) facilitate positive therapeutic outcomes and are associated with the entropy of EEG signals. Healthy individuals (N = 11) were administered 1 mg and 25 mg psilocybin 4-weeks apart. Confidence ratings for personally held beliefs were obtained before, during, and 4-weeks post-psilocybin. Acute entropy and subjective experiences were measured, as was well-being (before and 4-weeks post-psilocybin). Confidence in negative self-beliefs decreased following 25 mg psilocybin. Entropy and subjective effects under 25 mg psilocybin correlated with decreases in negative self-belief confidence (acutely and at 4-weeks). Particularly strong evidence was seen for a relationship between decreases in negative self-belief confidence and increases in well-being. We report the first empirical evidence that the relaxation and revision of negative self-belief confidence mediates psilocybin's positive psychological outcomes, and provide tentative evidence for a neuronal mechanism, namely, increased neuronal entropy. Replication within larger and clinical samples is necessary. We also introduce a new measure for examining the robustness of these preliminary findings and the utility of the REBUS model.

Characterising how perturbations of brain architecture influence brain function is essential to understand the origins of brain dysfunction, and devise potential avenues of treatment. Here we introduce a computational engine for systematic causal discovery of the functional consequences of altering network architecture and local biophysics in the brain. We integrate multimodal anatomical and functional neuroimaging to implement over 2, 000 in-silico brains, and provide mechanistic insight into the functional consequences of local lesions, global wiring, and empirically-derived maps of regional cytoarchitecture and chemoarchitecture. We comprehensively assess how each manipulation of brain macrostructure reshapes spatial and temporal signal coordination, information dynamics, and functional hierarchy—as well as spontaneous co-activation of meta-analytic cognitive circuits, and > 6, 000 dimensions of local neural dynamics. Our computational model systematically identifies which features of brain architecture have overlapping or antagonistic causal influence over each dimension of brain function, and how functional properties are traded off against each other across disorders and neuromodulation. We find that regions’ functional vulnerability to lesions in silico recapitulates their vulnerability to neurodevelopmental and psychiatric in vivo , along a core-periphery organisation. We provide convergent evidence that the brain’s wiring diagram is finely tuned to favour the hierarchical integration of information. Notably, our model successfully recapitulates known empirical results that have not been modelled before, including desynchronisation and flattening of the brain’s functional hierarchy induced by psychedelic 5 HT 2 A agonists. To catalyse future discoveries, we make this resource freely available to the neuroscience community through an interactive website (), where users can interrogate our systematic database of simulated cause-effect relationships. Altogether, we provide a powerful computational engine to predict the functional consequences of experimental or clinical interventions, and drive neuroscientific hypothesis-generation. ### Competing Interest Statement The authors have declared no competing interest.

Recent years have seen growing interest in the use of metrics inspired by complexity science for the study of consciousness. Work in this field has shown remarkable results in discerning conscious from unconscious states, and in characterizing states of altered conscious experience following psychedelic intake as involving enhanced complexity. Here, we study the relationship between complexity and a different kind of altered state of consciousness: meditation. We provide a scoping review of the growing literature studying the complexity of neural activity in meditation, disentangling different families of measures, short-term (state) from long-term (trait) effects, and meditation styles. Beyond families of measures used, our review uncovers a convergence toward identifying higher complexity during the meditative state when compared to waking rest or mind-wandering and decreased baseline complexity as a trait following regular meditation practice. In doing so, this review contributes to guide current debates and provides a framework for understanding the complexity of neural activity in meditation, while suggesting practical guidelines for future research.

High-order phenomena are pervasive across complex systems, yet their formal characterisation remains a formidable challenge. The literature provides various information-theoretic quantities that capture high-order interdependencies, but their conceptual foundations and mutual relationships are not well understood. The lack of unifying principles underpinning these quantities impedes a principled selection of appropriate analytical tools for guiding applications. Here we introduce entropic conjugation as a formal principle to investigate the space of possible high-order measures, which clarifies the nature of the existent high-order measures while revealing gaps in the literature. Additionally, entropic conjugation leads to notions of symmetry and skew-symmetry which serve as key indicators ensuring a balanced account of high-order interdependencies. Our analyses highlight the O-information as the unique skew-symmetric measure whose estimation cost scales linearly with system size, which spontaneously emerges as a natural axis of variation among high-order quantities in real-world and simulated systems. This paper introduces entropic conjugation as a new framework to analyse high-order interdependencies in complex systems, clarifying existing information-theoretic measures and revealing new ones. The framework allows to disentangle symmetric and skew-symmetric measures, highlighting the O-information as a unique, computationally efficient, and naturally emerging axis of variation of high-order interdependencies in real-world and simulated systems.