On the Neurodynamics of Consciousness: A Field Theory for Qualia and Intentional Objects

1. Introduction

The problem of consciousness, once the exclusive domain of metaphysics and classical philosophy, has emerged in recent decades as a central challenge for neuroscience and the philosophy of mind. While historical debates, ranging from Plato’s dualism to Aristotle’s hylomorphism and Descartes’ mind–body separation, have shaped our understanding of mental phenomena, the modern formulation of the problem is defined by the epistemological discontinuity and ontological separation between brain processes and subjective experience (Reale and Antiseri, 2003; Revonsuo, 2010; De Sousa, 2015).

Contemporary models often treat consciousness as an emergent property of neural activity, yet fail to provide a mechanistic account of how subjective phenomena, what-it-is-like (Nagel, 1974) or qualia, arise from biophysical dynamics. This tension is captured in two influential formulations: Chalmers’ Hard Problem (1996), which emphasizes the ontological discontinuity between physical states and phenomenal experience, and Levine’s Explanatory Gap, which stresses the lack of epistemic pathways linking neural correlates to qualitative states (Revonsuo, 2010). Despite the identification of numerous neural correlates of consciousness, these models remain fundamentally correlational and offer no causal framework to explain why and how specific patterns of brain activity generate conscious contents.

In response to this impasse, this work proposes a field-theoretical model in which consciousness is conceptualized as a nonlocal phenomenal field dynamically modulated by brain energy dissipation. Central to this proposal is the construct of neurentelechy, a thermodynamically grounded measure of energy dissipation associated with the instantiation of conscious content. Drawing on formal tools from neurodynamics, thermodynamics, and phenomenology, the model articulates a quantitative framework for mapping energy transformations in the brain to the structure of intentional experience.

The goal is not merely to correlate brain states with conscious phenomena, but to formulate a causal, testable bridge between them. The theory generates a set of empirical predictions, including the coupling energy hypothesis, which posits that conscious processing is marked by a measurable energy differential between metabolic and electromagnetic activity. This framework aims to dissolve the ontological discontinuity at the heart of the Hard Problem by positing consciousness not as an emergent anomaly, but as a structural invariant of nature, an ontologically fundamental field modulated by, but not reducible to, brain dynamics.

According to De Sousa (2015), the most well-known neural models of consciousness in the literature include: (1) Multiple Drafts (Dennett), (2) Somatic Markers (Damasio), (3) Neurodynamic (Freeman), (4) Global Workspace (Baars), Global Neuronal Workspace (Dehaene), and (5) Dynamic Core (Edelman). While some of these models acknowledge the importance of brain physiology in the emergence of conscious phenomena, their theoretical frameworks are primarily cognitive in nature, as seen in the models proposed by Dennett and Baars. In contrast, other models emphasize neurobiology in their theoretical constructs. Regarding the common features shared by these models, De Sousa (2015) highlights five key aspects: (1) the adoption of the concept of information as central; (2) the ontological thesis that the neuron is the basic unit of information processing; (3) the principle of neural interconnectivity; (4) the ontological thesis of brain modularity; and (5) the principle of information distribution across the brain. Additionally, De Sousa (2015) notes that all these models implicitly share the physicalist thesis, which posits the brain as a physical entity and the cause of consciousness.

Walter Freeman’s neurodynamic model appears to be one of the most promising regarding the solution of the Hard Problem. Freeman provides an original perspective on consciousness that requires the action of physical mechanisms driving brain physiology to enable the emergence of conscious experiences, forming a kind of causal continuum from physics to biology, and then from biology to psychology (Freeman, 2009, 2008, 2001, Freeman et al., 2015, 2003)⁠. In his approach, attractors constantly drive the brain toward lower energy states, producing patterns of brain activation that correlate with conscious experiences, detectable through techniques such as EEG (electroencephalography), fMRI (functional magnetic resonance imaging), and PET (positron emission tomography) (De Sousa, 2015; Freeman, 2001)⁠. Freeman also asserts that brain neurodynamics are governed by both linear and non-linear equations (Freeman et al., 2015)⁠. The concept of neurentelechy builds upon these neurodynamic principles, particularly in relation to dissipative structures (Prigogine, 2002), offering a mathematical representation of energy dissipation in the brain and its potential relationship with conscious experience.

Furthermore, for Freeman, the brain is an open system far from equilibrium and thus describable by Prigogine’s theory of dissipative structures (Prigogine, 2002)⁠. Applying this theory, it can be said that the brain constantly self-organizes as it receives energy from its external environment, which drives it even further from equilibrium. This energy can come from food, light, mechanical waves, etc. When the brain receives an energy influx that destabilizes it, its activation pattern undergoes a bifurcation. At this moment, the brain’s own history and energy fluctuations will cause it to reorganize, adopting one of many possible new structures or collapsing.

It is important to mention that Freeman himself admits he has not been able to postulate a causal mechanism to explain how brain physiology gives rise to conscious states (De Sousa, 2015; Freeman et al., 2015)⁠. This stance is commendable; however, unlike him, most other authors do not even bother to propose any causal mechanism. For them, the idea that the brain causes conscious states is taken as self-evident (De Sousa, 2015)⁠. As a consequence, their models are of the type: Z, at which point a miracle happens, then Q. Unfortunately, they focus only on establishing correlations and neglect to address the core of the modern problem of consciousness, the Hard Problem and the Explanatory Gap.

The lack of resolution for this core issue demonstrates that there is still much work to be done in order to solve the problem of consciousness. New scientific research focused on discovering the causal mechanisms of conscious states needs to be conducted. Only with these mechanisms well-described and tested through experimentation will it be possible to establish a general neuroscientific theory of consciousness.

1.1. Intentionality and Qualia

In philosophy of mind, intentionality is a technical concept introduced by medieval scholastics, bearing little resemblance to the colloquial sense of “intention” (Gunttenplan, 1994; Lyons, 1995; Mandik, 2010; Rakova, 2006)⁠. In the medieval approach, a distinction was drawn between (1) esse naturale, referring to natural existence, such as that of a mountain or a flower, and (2) esse intentionale, denoting intentional or mental existence, such as a thought or mental image. Regarding the latter, the term intentionale derives from the Latin root intentio, which can be roughly translated as “to have an idea” or “directing attention in thought” (Lyons, 1995)⁠.

In the 19th century, the German philosopher Franz Brentano reintroduced the term into the philosophical mainstream. According to his conception, intentionality is the hallmark of the mental, characterized by the mind’s directedness toward intentional objects, the real or imagined contents to which the mind can be directed (Gunttenplan, 1994; Mandik, 2010; Rakova, 2006)⁠. This means that mental acts, such as thinking and believing, always possess content: thinking is always about something, just as belief is always about something. This directedness of the mind toward an object is captured semantically by the notion of “aboutness”; intentional acts invariably possess content.

Linked to intentionality is the concept of intentional states, which are mental states or functions that contain intentional objects. These states include thoughts, beliefs, desires, emotions, etc. (Gunttenplan, 1994; Rakova, 2006)⁠. In the sentence, “John thinks about Mary”, the intentional state is the thought, and the intentional object is Mary. The same pattern applies to “Ivan wants to eat pizza”, where the intentional state is the desire to eat, and the intentional object is pizza. In both examples, the subjects’ minds are directed toward an object, illustrating intentionality, though the types of mental states, thinking and desiring, are phenomenologically distinct. Thinking is not the same as desiring. One can feel a desire without thinking about the desire itself, just as one can think of countless objects or beings, from personal desires to fantastical entities like unicorns or werewolves.

Over time, some authors have advocated reductionist approaches to intentionality (Gunttenplan, 1994). With the rise of behaviorism in the last century, attempts were made to equate intentional states to mere dispositions for behavior caused by environmental or internal stimuli (Gunttenplan, 1994; Revonsuo, 2010)⁠. Its founder, John B. Watson, argued ideologically that science should rely solely on directly and publicly observable data. Consequently, he concluded that consciousness could not be a scientific object of study, as conscious phenomena are not publicly observable. For Watson, such phenomena could not be understood in purely physical terms, relegating them to metaphysical entities outside the scope of science. In his view, psychology should study only public behavior and discard “metaphysical” concepts, as he deemed them, such as desire, volition, feeling, and thought (Revonsuo, 2010). Thus, addressing intentionality as traditionally defined by medieval scholars and Brentano would be unscientific.

Another reductionist approach to intentionality emerged from functionalism, regarded as one of the most significant frameworks for the mind-body problem, as it represented the first academic attempt to resolve it objectively. Functionalists criticized behaviorists for denying the mind’s existence and replacing it with behaviors and behavioral dispositions (Gunttenplan, 1994)⁠. According to U.T. Place, behaviorism produced an “intractable residue” of conscious phenomena by denying their reality, a nonsensical stance, given that every mentally sound human can perceive and describe their own thoughts, feelings, etc. (Gunttenplan, 1994; Place, 1956)⁠. The existence of these phenomena is evident in acts of thinking, feeling, and formulating arguments like this one; denying them is to deny reality itself.

For functionalists, the mind results from interactions between external stimuli and behavioral responses (Gunttenplan, 1994; Revonsuo, 2010)⁠. Mental states, in the functionalist model, are seen as functions of an information-processing system (Revonsuo, 2010)⁠. Within this framework, intentionality is understood in terms of causal relations: it is what causes mental states through external stimuli and, in turn, causes behavior (Gunttenplan, 1994). Functionalism introduced the computer analogy, likening the mind to software and the brain to hardware. Some functionalists claim that stimulus-response interactions are formally equivalent to algorithms the brain uses to determine responses to stimuli (Revonsuo, 2010). This idea is known as strong artificial intelligence or computational functionalism (Chalmers, 1996; Gunttenplan, 1994)⁠.

Like behaviorism, functionalism also has flaws. Its primary weakness, shared with behaviorism, is its reductionism, which strips away seemingly obvious characteristics described in classical definitions of mind and intentionality (Gunttenplan, 1994). Thus, neither model resolves the mind-body problem nor offers a valid naturalistic solution to the medieval and Brentanian concept of intentionality. Interactions between stimuli and responses cannot equate to thoughts, feelings, or other mental states, as mental states possess qualities (qualia), such as the sensation of red, pain, saltiness, sweetness, bitterness, pleasure, etc. (Mandik, 2010; Rakova, 2006; Revonsuo, 2010)⁠. One cannot open a brain and locate a quality. Qualia elude reductionist accounts the mind and intentionality. Because intentional objects are composed of qualia, any theory that ignores phenomenal properties fails to capture the full structure of intentionality.

Revonsuo (2010) emphasizes the indispensable role of qualia in consciousness, arguing that subjective experience would cease to exist without them. He describes qualia as the foundational elements of the “subjective stream” of psychological life, constituting the internal world of human consciousness. According to Revonsuo, qualia exhibit distinct characteristics: they vary in intensity (e.g., faint sounds versus vivid colors), are perceived within specific spatial and temporal contexts, and persist dynamically before fading from awareness. This temporal and perceptual dimensionality underscores their irreducibility to purely physical or functional terms (Revonsuo, 2010). This work adopts physicalism as a premise, much like the behaviorists and functionalists did, but in a distinct approach from these two.

2. Neurentelechy

Neurons, like any other cell type, need to produce large amounts of energy to maintain their functions. To achieve this, cellular metabolic processes convert energy substrates into usable units, ensuring the sustenance of neuronal activities. During this process, a gradient is generated that drives ion transport, enabling the production of energy in large quantities. Through these processes, brain cells generate an energy reserve, which, via specific ion transport mechanisms, makes it possible to maintain the resting potential across neuronal membranes. Upon receiving appropriate signaling, neurons fire action potentials, which can alter the activity patterns of the entire brain. It is through the firing and propagation of these action potentials that brain activity patterns correlated with conscious experiences are formed.

As the available energy is expended to restore the membrane potential of neuronal axons, additional energy must be generated to sustain the brain’s functions. This process causes the brain to oscillate over time between different energy states. At times, the brain increases its energy reserves; at other times, it depletes them. Since energy expenditure is required for the firing and propagation of action potentials, it is expected that conscious experiences occur when the brain is expending energy, or at the point immediately following an energy expenditure phase and immediately preceding an energy production phase. The following equation provides a theoretical description of the energy expenditure required for brain activity to be associated with the emergence of a conscious experience:

$$N_{\alpha } = E_{ t + 1} - E_{ t} + E_{\lambda }$$

(1)

This equation measures the absolute neurentelechy1 (N_α) between two adjacent time points. The variable N_α refers to the energy associated with the emergence of a conscious experience, whether quale or intentional object. E_t is the amount of the E (energy) in a time (t), E_t+1 corresponds to E in an even time after t, e E_λ represents the E of the background activity2. In this work, time zero (the origin) is arbitrarily defined as having lower energy than time one, leading to the implication that odd-numbered time points possess greater energy than even-numbered ones. This reflects the brain’s energetic oscillation. As a result of this equation, the value of N_α will be a negative number, corresponding to the loss of brain energy associated with the initiation and propagation of action potentials, that is, the performance of work capable of triggering the emergence of some content of consciousness. Thus, for neurentelechy to occur, the following requirement must be met:

$$E_{ t} > E_{ t + 1} + E_{\lambda }$$

In this model, all energetic terms, including E_α, E_ω, E_α, and S, are treated as dimensionless or expressed in arbitrary units. This convention aligns with standard practices in theoretical neuroscience and neural mass modeling, where the focus lies on relative variations in system dynamics rather than on absolute physical magnitudes. Although the formalism draws inspiration from thermodynamic and physical principles, it is embedded within a phenomenological framework aimed at capturing the informational and structural properties of brain–consciousness coupling. As such, explicit physical units (e.g., joules or watts) are not assigned, and their absence reflects a deliberate abstraction to preserve conceptual generality, mathematical tractability, and cross-domain applicability.

3. Bipartite Reality and the Neurodynamic Code

Neurentelechy can describe how the brain’s dynamics make it possible to perform work within consciousness. To ensure clarity for readers from different disciplines, the mathematical formalism will be introduced step by step, with explanatory examples. To contribute to solving this issue, consider the following thought experiments:

(1) Think of someone you love! Now, locate where in space your thought is situated! Where is it? At what point in space can the feeling of love be located?

(2) Reflect on what you were thinking before reading this sentence. Can you recall what you were thinking about 10 minutes ago?

The results of these experiments reveal something profound about the nature of conscious content. While it is possible to assert that a particular brain area is responsible for a certain thought, it is not possible to claim that thoughts are actually located at the spatial point where these regions exist. The possibility of spatially locating a cause does not imply the possibility of spatially locating its effect. This suggests that consciousness is not situated at any point in spatial dimensions. However, the fact that it is possible to temporally locate thoughts, even if imprecisely, conclusively shows that the phenomena of consciousness occur in time. These results support the inference that consciousness can be modeled as a nonlocal phenomenal field whose dynamic configurations correlate with patterns of neural activity. While subjective experience lacks spatial coordinates in the physical sense, the field itself appears to interact globally with the brain’s energetic landscape.

This work proposes the principle of bipartite reality as an explanation for the temporal occurrence of consciousness. According to this principle, reality is divided into two partitions: (1) “real space”, and (2) “virtual space”3. What characterizes “real space” is the presence of both time and space. Therefore, the objects located within this partition are objects that can be located in both the spatial dimensions and the temporal dimension. In contrast, in “virtual space” lie objects that occur solely in time. According to the bipartite reality principle, consciousness is not contained within the “real space” of the brain, but in its “virtual space”. This interpretation aligns with philosophical discussions on intentionality while providing a physicalist framework that connects neurodynamic processes with phenomenal consciousness. Although this bipartite principle was initially inspired by relativistic considerations, it is now interpreted as a representational tool. The notion of “virtual space” was reframed as a descriptive abstraction of a nonlocal consciousness field, rather than as a literal physical domain devoid of spatial dimensions.

The development of this model began with insights drawn from Einstein’s theory of special relativity, particularly his demonstration of how relative motion fundamentally links space and time, showing that as an object’s speed increases, time dilates while space contracts in the direction of motion (Einstein, 1905). This profound interdependence suggested that similar relationships might operate at different physical scales, including in biological systems. The original hypothesis proposed that the brain’s energy dissipation patterns could generate analogous space-time modulations at quantum or thermodynamic scales, creating subtle but significant distortions that might influence conscious experience. These theoretical space-time perturbations were envisioned as operating through temporal rather than spatial dimensions, potentially explaining how consciousness could emerge as a physically-grounded yet non-spatial phenomenon. This relativistic inspiration crucially established several foundational principles: that conscious experience need not be spatially localized to be physically realized, that energy dynamics play an essential mediating role between neural activity and phenomenology, and that temporal structure represents a fundamental characteristic of subjective experience. While these core insights remain valid and have been preserved in the model’s current formulation, the specific mechanism of space-time distortions has been superseded by a more comprehensive field-theoretical framework. The updated version replaces the original “virtual space” concept with a physically-grounded phenomenal field interacting with neural processes, transforms the space-time modulation hypothesis into a direct field-neural coupling paradigm, and generalizes the energy-based approach into a unified theory of consciousness as a fundamental property of reality.

The model posits a neurodynamic code transmitted via neurentelechy, initially described as energetic signatures in a “virtual space” interpreted by consciousness. In its current field-theoretical form, the interpretive mechanisms are replaced by fundamental field interactions, but the notion of information-bearing energy patterns mediating brain and experience remains essential.

The general equations of neurentelechy are based on equation (1). In this equation, absolute neurentelechy can be classified as either primary matrix type or secondary matrix type. Now, consider the equations:

$$M_{\alpha } ={\sum }_i^n{N}_{{\beta }_i}$$

(2)

$$M_{\beta }={\sum }_i^n{M}_{{\alpha }_i}$$

(3)

M_α refers to the value of the primary matrix neurentelechy, and M_β to the value of the secondary matrix neurentelechy. N_β is the basal neurentelechy associated with a single matrix position. In both equations, the results will be negative. This occurs due to the following equation:

$$N_{\beta } = E_{{\beta }_{t+1}} - E_{{\beta }_{ t}} + E_{{\beta }_{\lambda }}$$

(4)

The variable$E_{{\beta }_t}$represents the amount of energy of the matrix position in t,$E_{{\beta }_{t + 1}}$is the amount of energy of the matrix position in t +1, e$E_{{\beta }_{\lambda }}$is the E of background activity. From equation (4), consider the development of the general equations (2) and (3), respectively:

$$M\alpha =\left({\sum }_i^n{\left(E_{{\beta }_{ t + 1}} - E_{{\beta }_{ t}}\right)}_{ i}\right) + E_{{\beta }_{\lambda }}$$

(5)

$$M_{\beta }=\left({\sum }_k^{n\prime }{\left({\sum }_i^n{\left(E_{{\beta }_{ t+1}}-E_{{\beta }_{ t}}\right)}_{ i}\right)}_k\right)+E_{{\beta }_{\lambda }}$$

(6)

From equations (5) and (6), it is possible to determine the neurentelechy associated with the code of a content of consciousness. Therefore, the values of M_α and M_β are important for understanding the thermodynamic relationship between the brain and consciousness, as they represent the energy associated with the causation and the propagation of space-time distortions resulting from brain neurodynamics.

To understand the neurodynamic code, it is useful to imagine a system composed of two perfectly superposed and inseparable flexible sheets (Figure 1). The lower sheet represents “real space”, and the upper sheet represents “virtual space”. Thus, whenever an elevation appears on one of the sheets, it must also appear on the other at the exact equivalent points. By imagining several of these elevations arising over time from events occurring in the “real space” sheet, one could observe a landscape in the system full of elevations and flat spaces. This topology is analogous to a neurodynamic code matrix, and each elevation is analogous to a N_β. Therefore, the neurodynamic code for a content of consciousness is like a photograph, updated at each moment, of this transient landscape.

4. Qualia Vectors: The Driving Force of Consciousness

Intentionality, or the capacity of the mind to direct itself toward real or imaginary intentional objects, can be understood as a resultant force. In this perspective, intentionality is the result of the integration of several qualia within “virtual space”. Qualia vectors are the forces that direct consciousness toward qualia.

In this model, qualia are both the qualities described by philosophers of mind and the basic units of intentional objects that cannot be described as qualia in their strict philosophical sense. Once we consider all the parts that make up an intentional object as qualia, the possibility of decomposing intentional objects is evidenced by imagining a small red ball with the smell of strawberry (an intentional object). In this case, the intentional object is composed of at least two qualia: (1) the sensation of red and (2) the sensation of the smell of strawberry. These qualia triggered by sensory stimulation caused by the ball make up the intentional object. Therefore, if intentional objects are made of qualia, and intentionality is the direction of consciousness toward intentional objects, then intentionality is the resultant of the synergistic action of various qualia vectors.

If these conclusions are correct, then primary matrix neurentelechy acts as the fuel for qualia vectors, and secondary matrix neurentelechy as the fuel for intentionality. Thus, the energy present in “real space” in the form of neurentelechy is directly coupled to the phenomenal field, generating quale energy (E_q) or intentional energy (E_o), in the “virtual space”. The equations that describe these conversions are:

$$E_q = \left(- 1\right)\left(M_{\alpha } + S\right)$$

(7)

$$E_o=\left(-1\right)\left(M_{\beta }+S\right)$$

(8)

The variable S represents entropy. During the space-time distortion process triggered by brain activity, it is expected that part of the energy will be converted into entropy. Therefore, it can be inferred that the remaining energy is used in the “virtual space” a E_q and/or E_o. Based on these equations and equation (1), consider then:

$$E_{\omega } = \left(- 1\right)\left(N_{\alpha } + S\right)$$

(9)

$$E_{\alpha }=E_{ t+1}-E_{ t}$$

(10)

E_ω represents the energy present in the “virtual space” associated with the emergence of any content of consciousness, whether a quale or an intentional object. E_α is the total energy – neurentelechy and background activity – expended by the brain associated with the emergence of a conscious experience. Considering equations (1), (9), and (10), the following equation can be obtained:

$$E_{\omega } = \left(- 1\right)\left(E_{\alpha } + E_{\lambda } + S\right)$$

(11)

This is referred to in the present work as the general thermodynamic equation of the bipartite reality. Through equation (11), it is possible to describe the conversion of energy associated with the “real space” to energy associated with the “virtual space”.

The hypothetical neurodynamic code can be understood as a matrix code, where each position in the matrix is a value of neurentelechy correlated with a local space-time distortion caused by the neurodynamics of an arbitrary brain region. A set of matrix positions forms a matrix, which contains the neurodynamic code of a content of consciousness4. These contents can be encoded by a primary matrix, or by a secondary matrix, which is a matrix formed from the combination of two or more primary matrices. The primary matrices encode qualia, and the secondary matrices encode intentional objects. Each of the possible matrices has an associated amount of neurentelechy. For primary matrices, the neurentelechy is primary matrix neurentelechy, and for secondary matrices, the neurentelechy is secondary matrix neurentelechy. Both types of neurentelechy result from the association of several basal neurentelechies associated with matrix positions.

The energy transformations described in equations (9) through (11) establish the theoretical basis for a measurable criterion of brain – consciousness interaction. Appendix A formalizes this relation through the coupling energy hypothesis, defined as the energy differential between estimated metabolic consumption and observable electromagnetic dissipation during conscious states. This formulation introduces a falsifiable empirical signature of consciousness, compatible with experimental techniques such as fMRI, EEG, MEG, and PET.

5. Formalism for Simple Intentional Objects

In order to apply the bipartite reality model and test it empirically, a mathematical formalism for intentional objects is required. This work will focus solely on simple intentional objects, while future studies will address complex intentional objects. A simple intentional object is defined as a mental entity that can contain only one state per quale category, whereas a complex intentional object may have multiple states in each category. This means that a simple intentional object cannot, for instance, be simultaneously blue and yellow; it can only be blue with a certain intensity. This simplification facilitates the theoretical modeling and analysis of conscious contents.

An intentional object O can be represented as a vector in a vector space Rⁿ, where n denotes the total number of possible qualia. Each dimension of the vector correspond to a quale type, with the associated scalar value denoting its intensity. The intensity of different quale types is represented by the vector α, which determines the magnitude of q, according to the equation:

$$O={\sum }_c{\sum }_i{\alpha }^c{\delta }_i^c{q}_i^c$$

(12)

where c represents the quale category (e.g., “color”, “shape”), and i is the index of a specific quale within a category (e.g., “red” or “blue” in the “color” category). Additionally${\delta }_i^c\in \{0,1\}$acting as a binary selector, it selects only one quale per category, with 1 representing an active quale and 0 an inactive quale. The intensity is a value that can range between 0 and 1.

Based on this definition, three basic operations can be proposed to describe how intentional objects change within the “virtual space”: (1) Intensification, where the intensity of a quale is modified; (2) Transformation, which allows the substitution of one quale for another within the same category; and (3) Recombination, which adds or removes a category of qualia, enabling the intentional object to have more or fewer qualia. The equations for these operations are presented below, respectively:

$$O\prime ={\sum }_c{\sum }_i\left({\alpha }^c+\Delta {\alpha }^c\right){\delta }_i^c{q}_i^c$$

(13)

$$O\prime ={\sum }_c{\sum }_j{\alpha }^c{\delta }_j^c{q}_j^c\mathrm{with}{\delta }_i^c{\delta }_j^c=0$$

(14)

$$O\prime =O+{\sum }_{c\prime }{\sum }_k{\alpha }^{c\prime }{\delta }_k^{c\prime }{q}_k^{c\prime }\mathrm{with}c\prime \notin \left\{\mathrm{c}\right\}$$

(15)

where, in Equation 13, there is no summation over c. The idea here is that, at each time interval, some of these operations may occur, modifying the contents of consciousness and allowing its flow. These equations therefore capture, in a simplified yet structured manner, the fundamental dynamics of the “virtual space”, that is, of the human conscious mind.

Once the mathematical operations of “virtual space” have been described, it becomes necessary to establish their connection with “real space”, grounding the abstract structures of qualia and intentional objects in physically measurable quantities. To this end, a dynamic formulation is introduced to describe how energy flows from “real” to “virtual” spaces through intentional structure, without assuming thermodynamic equilibrium or stationary conditions. The approach adopted here is formally grounded in the tradition of neural mass models, which describe the mean-field dynamics of neuronal populations through differential equations. The use of this framework is intended to ensure compatibility with existing computational paradigms and to facilitate the implementation of simulations and the design of experimental validation protocols.

The basis of this connection lies in the transformation principle previously expressed in Equation 11, which establishes the relationship between the energy dissipated in “real space” and the energy manifest in the “virtual space”. Differentiating that equation with respect to time yields:

$${\displaystyle \frac{d{E}_{\alpha }}{dt}}=\left(-1\right)\left({\displaystyle \frac{d{E}_{\omega }}{dt}}+{\displaystyle \frac{d{E}_{\lambda }}{dt}}+{\displaystyle \frac{dS}{dt}}\right)$$

(16)

In this equation, E_α denotes the energy dissipated by neural activity in “real space”. E_λ corresponds to the energy involved in non-conscious, yet functionally relevant, neural processes, and S refers to entropy associated with functional disorganization. The term E_ω, in turn, represents the energetic content of the “virtual space”, and its time evolution must be defined with reference to the intentional structure active at each moment.

The emergence of conscious content is modeled as a nonlinear function of the sensory input qualified by the intentional vector:

$${\displaystyle \frac{d{E}_{\omega }}{dt}}={\left(1+exp\left[-\left({\sum }_c{\sum }_i{\alpha }^c{\delta }_i^c{E}_i^c+{\eta }_t\right)\right]\right)}^{-1}$$

(17)

Here,$E_i^c$represents the energy associated with the quale indexed by i and c, that is, the energetic cost, in the “real space”, of instantiating a particular quale in the “virtual space”. The sigmoidal form reflects the probabilistic and saturating nature of conscious emergence, while the stochastic component η_t allows for fluctuations in the selection of qualia under similar energetic and structural conditions.

Substituting Equation 17 into Equation 16 yields the following expression for the rate of energy dissipation in “real space”:

$${\displaystyle \frac{d{E}_{\alpha }}{dt}}=\left(-1\right)\left({\left(1+exp\left[-\left({\sum }_c{\sum }_i{\alpha }^c{\delta }_i^c{E}_i^c+{\eta }_t\right)\right]\right)}^{-1}+{\displaystyle \frac{d{E}_{\lambda }}{dt}}+{\displaystyle \frac{dS}{dt}}\right)$$

(18)

Equations 16 through 18 describe a minimal neural mass model based on energy dynamics, in which intentional structure governs the emergence of phenomenal content, and this emergence is energetically constrained by neural dissipation, non-conscious processing, and entropy production. The adoption of a neural mass model formalism allows this theoretical structure to be aligned with contemporary computational neuroscience, offering a mathematically tractable and numerically implementable set of equations suitable for simulations and predictive modeling.

The formalism introduced offers a mathematically consistent approach to modeling simple intentional objects, combining qualia-based structure with a neurodynamic framework derived from energy dissipation principles. By treating intentional configurations as modulators of energetic flows within a neural mass model, it becomes possible to express the emergence of conscious content in terms of physically grounded variables. This integration provides a quantitative pathway between phenomenological organization and measurable neural dynamics.

The structure of the model is amenable to empirical investigation and computational simulation. Functional neuroimaging techniques such as fMRI, EEG, and MEG may be employed to assess whether variations in neural energy dissipation correspond to shifts in intentional configuration as predicted by the dynamics of E_α. Psychophysical studies may further examine whether changes in perceptual intensity correlate with modulation patterns encoded in the intentional vectors. Additionally, computational implementations based on Equations 16 through 18 can be used to simulate the emergence and evolution of activation patterns consistent with the properties of simple intentional objects.

While currently limited to simple configurations, each containing at most one quale per category, the framework supports future generalizations to complex intentional objects, including multiple simultaneous qualia, hierarchical structures, and recursive transformations. This initial model focuses on simple intentional objects and foundational thermodynamic relations. Future work will generalize the framework to incorporate memory processes, multisensory integration, and operational definitions of entropy (S), aiming for tighter physiological correspondence. Combined with advances in empirical methodologies and modeling strategies, this approach represents a foundational step toward the construction of a formal neuroscientific theory of consciousness.

6. Discussion

The initial bipartite reality hypothesis represented a conceptual breakthrough in addressing the Hard Problem of consciousness and the Explanatory Gap, by overcoming the limitations of conventional neuroscientific models that restrict themselves to correlations between neural activity and conscious states. While models such as Freeman’s neurodynamic model (2001) describe oscillatory patterns associated with consciousness, and the Global Workspace theory focuses on information integration for conscious access, both fail to explain how physical processes produce subjectivity (De Sousa, 2015)⁠.

The trajectory of this model mirrors theoretical advances in physics: just as Einstein’s relativity subsumed Newtonian mechanics while preserving its empirical successes, the field-theoretical framework subsumes the original bipartite hypothesis. The early reliance on space-time metaphors served a pivotal role in shaping the model’s causal structure, but the nonlocal field ontology now provides a more robust and empirically addressable foundation

This transition from a relativistic-inspired mechanism to a field-theoretical ontology preserves the original model’s core insights while generalizing its physical foundations. Originally, the present model proposed a causal mechanism grounded in three pillars: brain thermodynamics, special relativity, and dissipative neurodynamics. However, it has since evolved into a more robust and coherent structure, abandoning its dependence on relativistic interpretation in favor of a field-theoretical ontology. In this refined framework, consciousness is conceived as a nonlocal phenomenal field modulated by neural activity. The concept of neurentelechy remains central, now reinterpreted as the energy involved in the coupling between the brain and the conscious field. The earlier assumption that consciousness arises in a temporal virtual domain, independent of spatial dimensions and modulated by space-time distortions from brain energy dissipation, is now reframed. The “virtual space” becomes a functional abstraction that represents configurations of the conscious field, rather than a literal ontological partition. This reinterpretation dissolves the need to invoke a collapse of spatial dimensions and aligns the model with known principles of field interaction.

Freeman’s (2001) neurodynamics serves as a basis, as both models share the premise that energy oscillations and brain self-organization are central to consciousness. The mathematical framework developed here (e.g., Equations 1, 7–11, 16–18) captures how energetic patterns relate to the evocation of qualia and intentional states. The framework assumes that the emergence of conscious content is driven by specific energy transformations associated with intentional structures and neuronal dynamics. This opens immediate empirical possibilities: neuroimaging techniques like fMRI and MEG may be able to test whether fluctuations in energy dissipation correspond to changes in the content or intensity of conscious experience, supporting the field modulation hypothesis.

From the standpoint of philosophy of science, the model gains robustness through its falsifiability. In line with Popper (1959) and Lakatos (1980), it makes the following testable predictions:

• Neurentelechy: Direct measurement of brain energy gradients during conscious experiences can confirm or refute the existence of this specific energy. If experiments fail to detect energy fluctuations correlated with the emergence of qualia, the neurentelechy hypothesis would be undermined.
• Neurodynamic code: The identification of matrix patterns in neuroimaging associated with specific qualia would validate the existence of a neurodynamic code. The absence of such patterns in empirical studies would be a strong counter-argument.
• Validity of mathematical operations (Equations 13-15): The equations for intensification, transformation, and recombination assume that changes in qualia follow specific mathematical rules. Computational simulations or psychophysical tests could verify whether changes in perceptual intensity (Equation 13) or substitution of qualia (Equation 14) correspond to subjective reports. Discrepancies between mathematical predictions and empirical data would invalidate the proposed formalism.
• Neurodynamic connection (Equation 18): This equation predicts that excitatory neural activity is modulated by the intensity of qualia. Neuroimaging experiments (e.g., fMRI, EEG, or MEG) could correlate brain activation patterns with variations in qualia. The absence of correlation or neural dynamics incompatible with the equation would refute the proposed connection.
• Excess entropy dissipation during conscious states: If the conscious field is ontologically real and interacts with neural processes, then this interaction must be accompanied by physical consequences. According to thermodynamic principles, all physical interactions result in changes in entropy. Thus, the model predicts that the total energy dissipated during conscious processing should exceed the expected baseline of energy consumption attributable solely to internal neuronal activity. Empirical verification of anomalous entropy production would provide indirect support for the field interaction hypothesis. Failure to detect such excess dissipation, would falsify the prediction and challenge the proposed coupling mechanism between brain and conscious field.

The fifth testable condition is further developed in Appendix A, where the theoretical basis for an energetic imbalance associated with conscious processing is formalized. This extension provides a framework for deriving specific testable conditions grounded in measurable neuroenergetic parameters, reinforcing the empirical applicability of the model.

These falsifiability points make the model scientifically valid, according to the criteria of Popper (1959) and Lakatos (1980). If validated, the model could not only contribute to solving the Hard Problem, but also redefine the relationship between matter and mind. If refuted, its legacy will lie in the courage to confront long-standing theoretical impasses. However, as proposed by Lakatos (1980), even if some hypotheses of the model are refuted, this does not necessarily imply the complete rejection of the theory. Instead, such refutations may lead to adjustments in auxiliary assumptions, allowing the theoretical core to be preserved and refined. This continuous refinement process is essential for scientific progress, especially in complex fields like consciousness. Regardless of its empirical outcome, the model opens new frontiers for the science of consciousness, inviting the academic community to explore, and perhaps rewrite, the boundaries between the physical and the phenomenal.

This model also opens the possibility of interpreting consciousness not merely as an emergent phenomenon, but as a fundamental property of reality, a nonlocal phenomenal field akin to physical fields such as the Higgs field. This is advanced as an ontological postulate rather than a directly testable empirical hypothesis: consciousness is conceived as a structural feature of spacetime, modulated, but not generated, by brain dynamics. This postulate is central to the internal conceptual coherence of the theoretical framework, as it accounts for the non-spatial yet temporally localizable nature of qualia, and for the fact that the brain modulates rather than produces conscious contents ex nihilo. In this view, the conscious field functions as a minimal ontological substrate upon which neurodynamic codes, mathematically formalized in the model, act to shape subjective experience.

In Lakatosian terms, the testable prediction 5 targets the hard core of the research programme, the postulated existence of a phenomenal field, and thus plays a decisive role in evaluating the scientific progressivity of the model. If verified, it would not only support the theoretical architecture but also provide an objective criterion for detecting the presence of consciousness in systems where subjective report is inaccessible, such as non-human animals, minimally conscious patients, or artificial agents. In this way, the model redefines the epistemic conditions for ascribing consciousness, advancing the project of grounding subjective phenomena in physically measurable parameters.

This perspective is grounded in ontological monism, wherein the subjective and objective domains are regarded as complementary manifestations of a unified underlying reality, a position anticipated in Spinoza’s ontology of substance and echoed in modern formulations such as Russell’s neutral monism (Russell, 1921; Spinoza, 1985, 1677)⁠. In this light, consciousness is not an anomaly to be explained away, but a structural invariant of the universe itself, calling for a paradigm shift at the intersection of neuroscience, physics, and philosophy.

The original formulation of the model, based on the ontological hypothesis of a bipartite reality, sought to resolve the Hard Problem by introducing a causal mechanism capable of linking brain activity and subjective experience via space-time distortions as a heuristic scaffold. This approach aimed to bridge the Explanatory Gap by proposing a structural intermediary between neural dynamics and qualia. In contrast, the current field-theoretical formulation does not merely seek a mechanistic link, but enacts an ontological shift, in which the very premises of the Hard Problem lose their applicability. Rather than resolving the problem, the model now dissolves it: by rejecting the assumption that consciousness must emerge from non-conscious substrates and instead positing it as ontologically fundamental, the Explanatory Gap ceases to pose a legitimate conceptual challenge. The demand for a bridge between the physical and the phenomenal arises only within dualist or emergentist ontologies, frameworks that the present theory explicitly transcends.

7. Conclusions

This work has introduced a theoretical framework in which consciousness is formalized as a nonlocal phenomenal field dynamically modulated by neural energy dissipation. At the core of this proposal is the construct of neurentelechy, a quantitative descriptor of energy gradients linked to the instantiation of conscious content. By employing a formalism based on indexed qualia vectors and intentional configurations, the model articulates a structured mapping between neural thermodynamics and phenomenal organization. Departing from correlational paradigms, this account provides a candidate mechanism with explicit empirical consequences. Chief among these is the E_c hypothesis, which posits that conscious states entail a measurable energy differential between metabolic input and electromagnetic output, potentially enabling an operational criterion for consciousness independent of subjective report. Beyond its empirical tractability, the model advances a non-dualist ontological stance wherein consciousness is not generated ex nihilo by neural computation but reflects the modulation of a pre-existing, structurally invariant field. As such, it reframes the Hard Problem not as an ontological impasse, but as a category error, dissolved rather than solved.