Four hundred years before Christ, Epicurus may had intuited the existence of modern Chaos, which he called "Clinamen", while observing the non-linearity of the Nature. And, he perceived its creativity, which gave rise to the entire Universe.

Chaos is the emergent property of Nature that “determines” its inherent and primary unpredictability which could be allegorically compared to irrational numbers, such as π = 3.14159… which is the ratio between the measure of a circumference’s length and its diameter.

Laplace was partially correct, because, as π appears in this simple arithmetic, it is the result of an absolutely deterministic process. But as an irrational number, π has infinite, completely unpredictable decimal places, such as a chaotic behavior. To know progressively more of π, it is necessary to solve it numerically through the circumference/diameter arithmetic.

In line with Laplace, the Universe may indeed be determined by a set of mathematical functions, as Nature has infinite irrational numbers like π, and infinite non-linear functions like the differential function of the logistic map discovered by May in the 1970s (Equation 2) (28):

Every atom in the Universe may be determined by several non-linear differential functions, which by no means implies predictability—or mechanism.

Through one of these functions, Edward Lorenz, a meteorologist and mathematician, conceptualized chaos in the 1960s upon the discovery of one of its most spectacular properties: the extreme sensitivity of chaotic dynamic systems to initial conditions (29). In a non-complex dynamic system, described by a system of linear functions like y=ax, the change in the value of a parameter a will produce a proportional deviation in the system’s evolution. In a complex system, small changes in the initial parameters, over time, produce progressively more unpredictable evolutions from the initial moment: the “Butterfly Effect.”

Chaos is an evident property at the microscale. In molecular systems, its expression is absolute, requiring a “statistical physics” to study these systems, as pioneered by Boltzmann and Gibbs: in the absence of certainties, we observe the possibilities and calculate the probabilities of the system’s evolution (24, 25).

The legacy of Boltzmann and Gibbs changed Science but was not enough to explain the relationship between Chaos and Nature. Why, at a macroscale, do the effects of Chaos seem to disappear in patterns such as tree leaves, quartz crystals, or human bones? From the probabilistic viewpoint of Boltzmann’s Statistical Mechanics, these are also infinitely improbable states. But, unlike heat flow against the current, these states appear everywhere.

From a physical perspective, Complex Systems are indissociable structures and processes whose components, though definable, maintain intricate connectivity through long-range correlations and direct interactions (19). However, their inherent holistic nature may not be sufficient for complexity, as information is also required. Information has a mathematical relationship with entropy (17), which in turn is related to system nonlinearities, primarily provided by chaos.

Without chaos and information, a hyperconnected Universe would likely resemble a supersymmetric crystal, where hydrogen molecules, stabilized by nuclear forces, interact with one another through gravity, forming a perfect network of equidistant and identical stellar bodies throughout the space-time fabric. On the other hand, if there were only chaos without either nuclear (short-range) or gravitational (long-range) connectivity, matter would likely form a diffuse and isotropic plasma cloud throughout the Universe, which could be perfectly modeled by the functions of Boltzmann-Gibbs statistical mechanics.

In this sense, without an optimal balance between order (connectivity) and chaos (unpredictability), complexity cannot emerge, and the system’s dynamics are neither creative, adaptive, nor evolutive and internally stable —nor healthy, as shall be understood in the following lines.

Neither of those imaginary universes are ours. Because from this chaos and connectivity, infinite patterns of order emerge in our Universe (ordo ab chao): the Earth’s orbit around the Sun, under the effect of gravity on an astronomical scale, as well as turbulence in the atmosphere forming a cyclone. These are manifestations of singular order that cannot be predicted by predetermined designs (or laws) or linear functions driven by fundamental forces. The leaves of a mango tree all follow a pattern; an order emerges from molecules and cells. But each leaf carries the evidence of Chaos in its singularity. Why do the untamed particles in one context manifest order in another context, when they are together giving shape to Nature?

These particles maintain connections between themselves, which can be local interactions, but also non-local interactions and correlations, like a series of falling dominoes, where the first has an absolute correlation with the last one. Or the effect of a neuron in the motor cortex on a muscle in the sole of the foot through a neuronal pathway and a neuromuscular synapse. In this sense, the force of gravity determines the connection between celestial bodies. These connections can form crystalline lattices, orbital systems, extremely simple if they are very strong. Conversely, where connections are inexpressive, “strong chaos” manifests, as in ideal gases.

Connections are the counterweight to Chaos, organizing systems where the components are restricted in their degrees of freedom, but still maintain enough freedom to collectively manifest, through self-organization, macroscopic states of order that locally reduce entropy. The mango leaf “emerges” through self-organization from a set of components naturally connected both at short and long distances.

We can understand the manifestation of Order from Chaos as the propagation of a non-linear perturbation in a region of the system that subsequently finds a state of entropic minimization (reduction of free energy)—an attractor: the complex system tends to self-organize into an energy-saving configuration.

Whirlpools and cyclones are a canonical image of attractors in chaotic systems, where energy dissipates, and the system finds stability. Other complex structures and organizations in Nature, like mango leaves or an enduring government, can be described as attractors when they dissipate energy, reduce entropy, and find stability. Both the driving machinery of a cellular flagellum with molecular rotors and stators (30), and the mental blueprint of the first mechanical turbine can be the manifestation of the same attractor in different contexts: one molecular, resulting from the self-organization of matter in the evolutionary process, and the other cognitive, resulting from the self-organization of neural activity in the process of mental representation. What many advocate as “intelligent design” might be the emergence of systematic and systemic patterns at the various scales and realities of a complex universe.

Thus, life, mind, and society are emergent phenomena that appear in the dance between chaos and order, through the intricate network formed in the intimacy of Nature’s structures and processes.

From the dynamics of chaos in complex systems, an adequate scientific definition for life, inspired by Ilya Prigogine’s work on dissipative systems, can be formulated (20, 21): life is an emergent dissipative phenomenon, the self-organization of a system complex enough to simultaneously manifest organization and unpredictability and evolve creatively and adaptively in the synergy between order (intrinsic connectivity) and chaos.

Accumulated evidence over decades demonstrates that pathological processes compromise the complexity of the organism (31–39). This perspective finds a masterful echo in the psychiatry of Henry Ey, who fundamentally defines mental disorder as a loss of freedom (40). In this theoretical framework, processes that uncontrollably increase chaos (like psychotic disorganization) and those that impose excessive and rigid order (like compulsive rituals) result in the same final consequence: the reduction of the system’s adaptive complexity (36).

It is possible that the compromise of complexity could scientifically describe a new psychopathology in suffering minds, allowing investigation into whether and how mental “diseases” exist. And if they do, what are they like? To this end, we need to physically describe complexity.

The American scientist Josiah Gibbs (25), who with Boltzmann discovered and formalized Statistical Mechanics, opened a parenthesis in the successful history of his physics of probabilities (which explains non-linear phenomena on a micro-scale in causal relation to the macroscopic states of systems): his equations could not explain all the probabilistic dynamics of Nature. They work well for ideal gases and analogous systems, but not for some other cases.

These “some other cases” are the vast majority of dynamic processes in the Universe. And, in fact, ideal gases and others under specific regimes of temperature and pressure (from atmospheric air to stellar hydrogen plasma) are the special cases. What is common are storms and ocean currents (turbulences), anthills and beehives, schools of fish and flocks of birds, distinct and individual molecules perfectly correlated to manifest orders in various dimensions, from the cell to the entire biosphere with epidemics and cities, air traffic, and the Internet.

Since correlations exist in complex systems, their components cannot be treated statistically as independent. The non-ergodic dynamics that characterize such systems cause the entropy manifested in them to evolve distinctly, diverging from traditional thermodynamic models, which generally assume an ergodic exploration of the state space (16, 19). What determines, in a few words, a different prediction about the Universe than what the first statistical physicists proposed?

Constantino Tsallis is a naturalized Brazilian who, almost 40 years ago, wrote the article Possible Generalization of Boltzmann-Gibbs Statistics (42), where he innovatively proposed a set of mathematical functions that would statistically model dynamic systems in general, including ideal gases, which are well-described by Boltzmann and Gibbs Statistical Mechanics. Complexity, on the other hand, becomes maximum when there is long-range correlation and interaction between the components of a system. There is a statistical dependence between the behavior of these components. Hence, the entropy of a complex system is defined by Tsallis (42) through the following entropic functional:

Where q is a non-extensivity parameter that describes the non-independence among the system’s components, determining consistent probabilities (Equation 3). That is, Tsallis proposed a theory that generalizes the Statistical Physics previously proposed: Non-Extensive Statistical Mechanics, or simply q-Statistics (16, 19). The core of NEMS lies in the consideration of the mutual interdependence among the system’s components and thus its complexity. This complexity is quantitatively related to a conditioning parameter, “q”. At minimum or negligible complexity, the value of q → 1. When q > 1 in many models, we can infer a progressively more complex system as the value of q increases.

Over the years, experimental physics, engineering, sociology, economics, biology, etc., have shown the predictive power of q-Statistics for modeling phenomena such as quantum entanglement, tumor growth, critical cosmological systems (through delta-statistics), the evolution of the financial market, epidemics, and structure ruptures, among countless cases (e.g., 16, 19).

Our group has demonstrated the application of q-Statistics in modeling the dynamics of neural activity in the human brain on meso- and macroscopic scales, through EEG, which is notoriously complex (43). The regularity of the EEG signal, which represents the dynamics of possible brain states, is the parameter of analysis: we extracted the time intervals between events with amplitudes exceeding -1.00 standard deviation from the mean of the negative part of the signal (Figure 1, top). Instead of quantifying the entropy of the extracted inter-event interval series, we performed an empirical probability distribution of the occurrence of these intervals in histograms with 100, 500, and 1000 time interval classes (for example, 200 classes to intervals between 1 and 5 milliseconds, between 5.1 and 10 milliseconds, and so on). We fitted a q-exponential probability function developed by Tsallis (43) to the empirical distribution (Figure 1, bottom), and from best fitting, the function parameters are obtained, among them, the q value.

This function is given by:

Where, in addition to q, the parameters c, b, and h must be determined numerically such that they best fit the function over a probability distribution of events of the system in question (43). These events are regularities of the EEG signal given by intervals between amplitude events less than -1 standard deviation of the signal. If EEG were a purely chaotic phenomenon, the distribution of the probability of occurrence of each interval should be modeled by the exponential function of traditional Boltzmann-Gibbs statistical mechanics:

But since EEG is a complex phenomenon, the function in Eq. 4 faithfully represents the probability distribution. In both eq. 4 and 5, the parameter a is analytically determined by a gamma function that predicts the total area under the curve equal to 1 – probability density function.

This q-exponential function that has described the complexity of the typical and neurodivergent brain with great sensitivity (44), demonstrating, for example, the phenomenon of reduction of neural complexity in EEG of all brain throughout natural aging, or the effect of different functional states (such as listening to a favorite song or performing an attentional task) on the complexity in specific brain sites (45).

In this sense, assuming that the complexity of a biological system decreases in pathological states (just as it decreases in aging), as several authors have demonstrated (33, 34, 46), could q-Statistics reveal whether a state of suffering or mental divergence is pathological, based on the measurement of the extracted parameter q?

Undoubtedly, from a mathematical perspective, the absolute values of q will depend to some extent on the experimental design, which defines the EEG signal resolution, the bounds of the function-fitting algorithms for empirical distributions, the resolution of these distributions, and so forth. Therefore, establishing the optimal configuration for any experiment and standardizing this setup remain the primary challenges for the universalization of this measurement, as it is inherently relative to this configuration of parameters. This is a milestone for a possible clinical validation and medical application of q-Statistics in the future, in parallel with the systematic observation of the relationship between the q parameter and the brain dynamics of typical, neurodivergent, critical (although still adaptive and healthy) and mentally disordered individuals, regarding their demographic profiles, in different cultures and societies.

The treatment of high-frequency (muscular) and low-frequency (eye movement) artifacts has not shown a significant influence on q-values concerning the adopted bin size and range for empirical distributions of inter-event intervals (45), although they should always remain a central concern for the interpretation of results. The choice of the threshold (-1 standard deviation) adopted in our studies is justified by the Central Limit Theorem from the perspective of q-statistics, in which the tails of Gaussian and q-Gaussian functions clearly diverge (19). Consequently, by establishing this threshold for events that exceed the central limit of the statistical model, the sensitivity for identifying complex dynamics may be increased (43).

In the physics of complexity, every system has critical regions or moments where/when disorder (entropy) increases, and the system must find a new attractor—a new configuration of states that re-stabilizes the dissipative system. Criticality can be spontaneous or result from interaction with other systems. In fact, it is criticality that allows the system’s adaptive evolution and the emergence of diversity (14, 47).

From the viewpoint of the Complexity Paradigm, the mental crisis can be a process of adaptive transformation of a system, while suffering is commonly the experience of the crisis, therefore a normal phenomenon of transformation and adaptation processes. Psychology historically recognizes crisis as a potential for adaptation, evolution, self-knowledge, and development of the psyche, and the emancipation of the individual acquiring their autonomy and self-determination passes through these processes (9, 48–50). From an empirical standpoint, studies correlate the adaptive stress response in healthy organisms with a transient increase in complexity (51–53). The allostatic response, which produces a deviation from the organic baseline, can logically correspond to subjective phenomena of suffering and discomfort. This is evident in common experience—for instance, in situations of physical discomfort under strenuous demand or psychic tension when solving everyday problems. Therefore, differentiating adaptive stress, which is consistent with a physiological allostatic response, from maladaptive stress, related to allostatic overload, remains a challenge in clinical practice, especially in psychiatry.

The perception of crisis as a pathological process that must be suppressed establishes a real risk for the individual’s evolution and, perhaps, for all of humanity. The suppression of crises is often achieved through drugs that modulate the stress response, such as anxiolytics or antidepressants (54, 55). These drugs are not curing diseases, but rather anesthetizing human experiences that should be worked through based on their subjectivity (56, 57).

The human individual is a singularity that extends beyond their material limits (49). The manifestation of new states of order (new attractors) stemming from a crisis occurs in longitudinal correlation (historical and current) with the world the individual lives in (50). In fact, our subjectivity is a complex that involves the world that interacts with and correlates to us. Therefore, like any complex, we are an inseparable part of a larger world, just as we are an inseparable collectivity of smaller parts. And so, successively, in both directions. We are part of a universal fractal.

Thus, the unfolding of the crisis must pass through these two dimensions: the microscopic (internal and biological) and the macroscopic (ecological, social, and cultural). In the 17th century, Spinoza wrote an “Ethics” that centers the role of affect (power to affect and be affected), that is, connections and correlations, where bodies indeed become a circumstance of their relations (58). Spinoza’s Ethics was a disruptive view in its time, contemporary to the Cartesian TSM, about the nature of things, including a God “emerging” from all bodies in “affection.” Spinoza was a philosopher of complexity, of a fundamental and paradigmatic philosophy that can unfold into a dynamic and equally complex mental health practice, to which the philosopher Paulo de Tarso Peixoto contributes, developing a “Physiology of Contact” and a “Psychopathology of Complexity” (49). Just as the integral of the atom comprises the Infinite (59), we are an inseparable part of an integral Universe, distinguishable from the whole like a wrinkle in a sheet, where unpredictable phenomena are also the primary cause of Nature’s dynamics.

From the viewpoint of Positivism, the classic Enlightenment scientific philosophical doctrine that guides biomedical rationality to this day, the CP is not recognized. Its mechanistic models, instrumentalized by the TSM, are still the biomedical objective in psychiatry, however much failure imposes itself. Thus, an initial epistemological error was denounced by the philosopher Canguilhem (1966): the fragility of the dichotomous binomial normality-disease, establishing him as one of the most important thinkers for human health, with special interest in mental health.

Like Spinoza, Canguilhem reveals a second philosophy of Complexity when he questions that pathologies and normality are defined based on normative parameters already established in physiology and, by corollary, also in social and moral norms, proposing, alternatively, that normality in the clinical universe is related to an organism’s capacity to oppose established norms (60). Discussing from this point, normality is related not to crisis, but to the individual’s potential to adapt and evolve from the crisis, finding a new attractor through emergence—autopoiesis.

The capacity to oppose already established norms (including physical ones) reveals the potential for adaptation and creative innovation that a complex individual is capable of developing within a biopsychosocial context. Not so rarely do we observe people who existentially begin to live after the diagnosis of intractable cancer. Normality must transcend the mechanical and stationary perception of life. According to positivist normality, evolution and diversity would be impossible. Every evolutionary leap begins with a born anomaly, which experiences tension (sofrimento) in the current state and seeks (and finds) a new contextualized state, where it thrives divergently and amplifies the potencies of humanity as a whole.

Under the epistemological and methodological limits of the TSM that impose its blatant insufficiency, psychiatry adopted a new nosology under a phenomenological rationality, systematizing the recognition of mental syndromes, which are classified in the DSM and ICD diagnostic manuals. As already mentioned here, this new nosology moved away from the once unshakable mechanistic and reductionist view when it contextualizes phenomena, for example, within culture—formally, the report of hearing voices from beyond in one cultural and social context is hallucination, in another, it is mediumship (61, 62).

However, the classification of a syndrome of clinical interest—or a Mental Disorder—is based on the assessment that it causes significant suffering and impairment across multiple life contexts. Such a conclusive perception must be grounded in a literally complex clinical act, involving an understanding of the individual through intersubjective interaction between the clinician and the subject, which typically requires a significant amount of time. Even then, the dichotomous categorization of Health versus Disorder can be a trap; at times, it is impossible to determine with certainty whether a crisis is adaptive or maladaptive, or whether it is endogenously triggered or—as presupposed by Complex Thought—is a phenomenon shaped by hegemonic cultural values and social constraints acting upon singular endogenotypes. In a snapshot, an individual may violently suffer when losing a job or facing the prospect of war; however, within their longitudinal existence (past and future), there lies the potential for reinvention, opposition to norms, and reorganization into a new attractor.

As a mere illustration, we bring up that in any discipline of innovation (and entrepreneurship), there is a consensus that every technological solution comes from the anguish of experiencing a problem (63). Surely, innovation, whether in the subjective/existential territory or dependent on problems and crises. However, not every crisis, in fact, will unfold into innovation. It is probable (and often, highly probable) that a critical point will lead the system to absolute disorder, maximum entropy—what we would call death.

The challenge of Psychiatry is to find a way to characterize the meaning of the suffering and the multidimensional impairments that the individual experiences in the occurrence of a syndrome to design the most appropriate intervention: from guidance and counseling to pharmacological and hospital intervention.

At this moment, we find in the physics of Tsallis’ Complex Systems an opportunity to develop a feasible solution that assists the clinician in their conduct and contributes to the understanding of the crisis being observed.

Over the decades, with the advancement of complexity science, numerous methods have emerged based on information-theoretic analysis (e.g., the traditional Lempel-Ziv method for Kolmogorov complexity, see 64) and chaos quantification (especially through the calculation of the Lyapunov exponent in nonlinear series, see 22, 65). In this scenario, entropy measures such as Sample and Approximate entropies (66), as well multiscale strategy for entropy estimation (18), are pivotal for making inferences regarding a system’s complexity. However, these commonly adopted methods rely on Shannon/Boltzmann-Gibbs entropic functions. Although they demonstrate adequate performance in many contexts, they fail to account for the non-additive nature of complex systems, which are inherently non-extensive. Consequently, classical formulations of entropy remain insensitive to the fundamental properties that define a system as truly complex.

Tsallis’ Complexity has been treated as a physical measure that synthesizes the complexity of a dynamic system (16, 19), such as the human brain (14). Since pathological states generally seem to reduce the complexity of a system, just as aging does, might it be possible for disadaptive (pathological) conditions of the mind to be synthetically inferred by the reduction of the complexity of the cerebral dynamics recorded in the EEG? This inference is synthetic and comprehensive, because Complexity is a property, not a physical force or mechanism.

This is our current scientific question, still unanswered: how does mental suffering interfere (if it interferes) with the Complexity estimated by the parameter q in the EEG in various different functional states? The premise being that the reduction of complexity (evidenced by the value of parameter q) correlates with disadaptive critical processes that would more likely lead the system to collapse rather than to reorganization through the stabilization of a new attractor.

Interestingly, we find, in line with other studies (67, 68) that neural complexity seems to be higher in children diagnosed with ADHD (44). And unpublished data from adults with an inattentive/hyperactive profile denoted through screening by the Adult ADHD Self Report Scale seem to corroborate this finding. However, the studied adults in this sample do not manifest impairment or suffering related to the inattentive and hyperactive characteristics. The specific meaning of this finding is not the object of this essay. Although, based on the criticisms pointed out against conventional psychiatry and in the light of Canguilhem, we may be demonstrating a potentially adaptive neurodivergent pattern that gained a pathological character due to the positivist bias of a nosology based on pre-established norms. Despite its resonance with other studies, these preliminary evidences regarding the sensitivity of q-Statistics in discriminating different mental profiles and states must be systematically validated through further research. Future studies employing diverse approaches are necessary to ensure with certainty that unforeseen extrinsic biases are not responsible for these findings.

Currently, we are collecting EEG data from adults and children with various mental conditions (Schizophrenia, PTSD, disadaptive disorder, autism spectra) and hope soon to be able to verify how neural complexity behaves in these populations, envisioning the possibility of understanding critical human and neurodivergent conditions, corroborating a psychopathology of complexity (49) and, perhaps, establishing a method for clinical assistance.