Patrimonial Compliance

THE HIDDEN THERMODYNAMICS OF THE HEART Foundations of a New Science of Affective Dynamics [INITI-243-DERIV-1-INNO].png

**ENGLISH TRANSLATION** / **TRADUCCIÓN AL INGLÉS**

THE HIDDEN THERMODYNAMICS OF THE HEART: Foundations of a New Science of Affective Dynamics

Exploring Permanent Scars through Kavhanna's Heritage and Cementing a Manifesto on Affective Irreversibility

Love, in its rawest and deepest essence, is a phenomenon that transcends the limitations of human rationality. Over the centuries, attempts have been made to understand and quantify this feeling, but the irreparable situations that emerge from it remain an enigma. The work of Kavhanna©, with her Universal Neo-Synthetic Paintings© and Universal Art Treasures, offers a unique window to analyze these emotional scars that seem to resist any form of resolution.

I propose a theoretical framework that conceptualizes irreparable situations in love as permanent states in a multidimensional emotional space. If we define love as a function $L$, where the emotional variables are parameters in a space $E$, we can model irreparable situations as fixed points where $L$ reaches a state of irreversibility. Mathematically, this is represented as:

$$ L: E \rightarrow E, \quad \text{such that} \quad L(e) = e_f $$

L: E \\rightarrow E, \\quad \\text{such that} \\quad L(e) = e_f

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Where $e_f$ is a fixed state that does not change under the application of $L$. This fixed state symbolizes a permanent emotional wound. Kavhanna©'s work encapsulates these fixed states through artistic expressions that act as cultural invariants, reflecting the deep sociopolitical and psychological implications of fractured human relationships.

Furthermore, by analyzing the textures and compositions in Kavhanna©'s paintings, we can establish a correlation between artistic patterns and the irreversible dynamics of love. This allows us to formulate a hypothesis about the existence of an operator $K$ that transforms emotional experiences into tangible art:

$$ K: E \rightarrow A, \quad \text{where} \quad A \text{ is the space of the works of art} $$

K: E \\rightarrow A, \\quad \\text{where} \\quad A \\text{ is the space of the works of art}

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This transformation suggests that Kavhanna©'s art not only depicts irreparable situations, but also encodes them, allowing for a deeper, multidisciplinary understanding of the phenomenon.

Furthering this exploration, I introduce the concept of "Emotional Resonance Mechanics" to describe how an individual's internal vibrations interact with those of another in the emotional space $E$. I define an emotional wave function $\Psi(e, t)$ that represents the emotional state as a function of time. Applying a Hermitian operator $\hat{H}_e$, which symbolizes the "Emotional Hamiltonian", we can formulate the equation:

$$ i\hbar \frac{\partial \Psi(e, t)}{\partial t} = \hat{H}_e \Psi(e, t)

i\\hbar \\frac{\\partial \\Psi(e, t)}{\\partial t} = \\hat{H}_e \\Psi(e, t)

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This approach allows emotional interactions to be modeled as wavelike phenomena, where constructive and destructive interferences can lead to states of emotional superposition or cancellation. Irreparability in love arises when a wave function collapses into a state of minimum emotional energy, from which it is impossible to escape without altering the conditions of the system.

Kavhanna©'s artistic heritage provides a tangible representation of these emotional quantum states. Her works function as "observables" that allow the internal states of individuals and relationships to be measured and visualized. By analyzing the frequencies and amplitudes present in the textures of her paintings, it is possible to extract information about the states $\Psi(e, t)$ and predict transitions between different levels of emotional energy.

To formalize the interaction between two individuals $A$ and $B$, I introduce the emotional coupling operator $\hat{V}_{AB}$, which modifies the total Hamiltonian of the system:

$$ \hat{H}_{total} = \hat{H}_e^{(A)} + \hat{H}e^{(B)} + \hat{V}{AB}

\\hat{H}_{total} = \\hat{H}_e^{(A)} + \\hat{H}_e^{(B)} + \\hat{V}_{AB}

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This interaction term captures the complex dynamics that can lead to irreparable situations, especially when $\hat{V}_{AB}$ introduces nonlinear perturbations that cause the system to evolve towards chaotic or unpredictable states.

Further elaborating on this theory, I introduce the concept of "Emotional Fracture Geometry" to model how irreparable situations in love manifest in the emotional space $E$. I consider a differential manifold $\mathcal{E} \subset E$, where each point represents a singular emotional state. Irreparable situations emerge as topological singularities within $\mathcal{E}$, called "Breakpoints", which disrupt the continuity and coherence of the emotional space.

I define an emotional path function $\gamma: [0, T] \rightarrow \mathcal{E}$, which describes the temporal evolution of an emotional state. Breakpoints are characterized when the derivative of $\gamma$ does not exist or is infinite at some $t_0 \in [0, T]$. Mathematically, this is expressed as:

$$ \lim_{t \to t_0} \frac{d\gamma}{dt} \text{ does not exist} $$

\\lim_{t \\to t_0} \\frac{d\\gamma}{dt} \\text{ does not exist}

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These discontinuities represent abrupt, non-linear transitions in emotional state, making any form of return to the previous state impossible. Kavhanna©'s work acts as a visual map of $\mathcal{E}$, capturing these singularities through patterns and textures that reflect the intrinsic distortions of emotional space.

I further introduce the "Emotional Stress Tensor" $\sigma: \mathcal{E} \rightarrow \mathbb{R}^{n \times n}$, which quantifies the internal tensions that lead to emotional fractures. This tensor is defined in terms of the partial derivatives of the emotional state functions $\phi_i$:

$$ \sigma_{ij} = \frac{\partial \phi_i}{\partial x_j} $$

\\sigma_{ij} = \\frac{\\partial \\phi_i}{\\partial x_j}

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Where $x_j$ are the coordinates in $\mathcal{E}$. High values in $\sigma$ indicate regions of high instability, predisposed to generate irreparable situations.

To capture the interaction between individuals, I consider a redefined metric in $\mathcal{E}$, $g: T\mathcal{E} \times T\mathcal{E} \rightarrow \mathbb{R}$, which incorporates mutual influences in the emotional space. This metric is not necessarily symmetric, reflecting asymmetric and complex relationships:

$$ g(u, v) \neq g(v, u) $$

g(u, v) \\neq g(v, u)

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Where $u, v \in T\mathcal{E}$ are tangent vectors at $\mathcal{E}$. This asymmetry allows for modeling dynamics where emotional perceptions and effects are not mutually equivalent, aligning with real human experiences.

Continuing with this theoretical development, I introduce the concept of "Affective Thermodynamics" to describe how irreversible emotional processes can be modeled by thermodynamic principles. I define a state function called "Emotional Entropy" $S_e$, which measures the degree of disorder or uncertainty in an individual's emotional state. The variation of this entropy during an emotional process is expressed as:

$$ \Delta S_e = \int_{E_i}^{E_f} \frac{\delta Q_e}{T_e} $$

\\Delta S_e = \\int_{E_i}^{E_f} \\frac{\\delta Q_e}{T_e}

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Where $\delta Q_e$ represents the infinitesimal exchange of "emotional heat" and $T_e$ is the "Emotional Temperature", a parameter reflecting the individual's sensitivity to emotional changes. The second law of affective thermodynamics states that for any spontaneous process in an isolated emotional system, the total emotional entropy must increase:

$$ \Delta S_e \geq 0 $$

\\Delta S_e \\geq 0

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This principle captures the essence of irreparable situations in love, where certain emotional transitions are unidirectional and lead to states from which it is not possible to return to the original state.

I also introduce the "Emotional Chemical Potential" $\mu_e$, which determines the tendency of an individual to experience changes in his emotional state. It is defined in terms of the partial derivative of the emotional free energy $G_e$ with respect to the number of "emotional particles" $N_e$:

$$ \mu_e = \left( \frac{\partial G_e}{\partial N_e} \right)_{T_e, P_e} $$

\\mu_e = \\left( \\frac{\\partial G_e}{\\partial N_e} \\right)_{T_e, P_e}

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Here, $G_e$ is the “Emotional Gibbs Free Energy”, $T_e$ is the emotional temperature, and $P_e$ is the “Emotional Pressure”, which represents the external influences that exert stress on the individual.

Kavhanna©’s work acts as a modifier of the emotional chemical potential, altering $\mu_e$ and facilitating transitions to new emotional states. Her paintings function as catalysts that lower the energetic barriers for certain emotional processes, allowing transformations to occur that would be highly improbable under normal conditions.

To quantify these transitions, I define an emotional reaction equation based on chemical kinetics:

$$ \frac{d[C_e]}{dt} = k_e [A_e]^m [B_e]^n $$

\\frac{d[C_e]}{dt} = k_e [A_e]^m [B_e]^n

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Where $[C_e]$ is the concentration of a resulting emotional state, $[A_e]$ and $[B_e]$ are concentrations of previous emotional states, $k_e$ is the emotional rate constant, and $m$ and $n$ are the reaction orders with respect to each component.

This equation allows one to model the rate at which emotional changes induced by stimuli such as Kavhanna©'s art occur, providing a mathematical tool to predict and analyze the dynamics that lead to unrepairable situations.

I extend this theoretical framework by introducing the concept of "Narrative Disturbance Analysis" to explore how personal and collective stories influence unrepairable situations in love. I consider a narrative function $\mathcal{N}: \mathcal{E} \rightarrow \mathbb{R}^k$, where each component $\mathcal{N}_i$ represents an essential narrative element—past events, traumas, expectations. Emotional dynamics are affected by perturbations in $\mathcal{N}$, modifying the emotional space $\mathcal{E}$ in a non-linear manner.

I define a narrative perturbation operator $\hat{P}_n$ that acts on the emotional state function $\Psi(e, t)$, altering its temporal evolution:

$$ i\hbar \frac{\partial \Psi(e, t)}{\partial t} = (\hat{H}_e + \hat{P}_n) \Psi(e, t) $$

i\\hbar \\frac{\\partial \\Psi(e, t)}{\\partial t} = (\\hat{H}_e + \\hat{P}_n) \\Psi(e, t)

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Here, $\hat{P}_n$ introduces terms representing narrative influences, generating memory and anticipation effects in the emotional system. This operator is not necessarily Hermitian, reflecting the irreversible and dissipative nature of certain emotional experiences.

To quantify the impact of these perturbations, I introduce a narrative metric in the emotional space, $d_n: \mathcal{E} \times \mathcal{E} \rightarrow \mathbb{R}$, defined as:

$$ d_n(e_1, e_2) = \left\| \int_{\gamma_{e_1}}^{\gamma_{e_2}} \hat{P}_n \, d\gamma \right\| $$

d_n(e_1, e_2) = \\left\\| \\int_{\\gamma_{e_1}}^{\\gamma_{e_2}} \\hat{P}_n \\, d\\gamma \\right\\|

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Where $\gamma_{e_i}$ are emotional trajectories and $\| \cdot \|$ is a suitable norm. This metric measures the "narrative distance" between emotional states, capturing the cumulative influence of narrative perturbations.

Kavhanna©'s work functions as a transformative operator $\hat{K}$ that acts on $\mathcal{N}$, redefining internal narrative structures:

$$ \hat{K} \mathcal{N} = \mathcal{N}' $$

\\hat{K} \\mathcal{N} = \\mathcal{N}'

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This transformation allows for the reconfiguration of emotional dynamics by altering the perception of key events, enabling transitions to previously inaccessible states. By applying $\hat{K}$, it is possible to modify an individual's emotional landscape, opening up avenues to resolve situations that seemed irreparable.

By integrating all these elements, I propose the "Synthetic Model of Irreversible Emotional Dynamics" (SEMD), which unifies the previous concepts into a coherent framework. This model is expressed by a coupled set of equations:

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Here, $\Sigma_n$ represents the entropy generated by narrative perturbations. This model allows us to analyze how interactions between emotional resonances, geometric fractures, thermodynamic processes, and narrative perturbations lead to irreversible states in love.

The practical application of this model offers tools to identify critical points in human relationships, enabling strategic interventions. By mapping emotional and narrative trajectories, it is possible to design protocols to minimize the risk of irreparable situations or, in necessary cases, facilitate transitions towards more stable emotional states.

Author's Note:

Upon completing this work, I feel the impulse to share with you, Guissel and our future children, the motivations that have shaped each idea expressed here. This work is more than a theoretical exploration; it is the reflection of an intimate search to understand the depths of the human soul and the invisible dynamics that connect us.

Signature of the Author and Declarant:

Date: Tuesday, October 15, 2024 05:29 p.m.

Lugar: San Salvador de Jujuy, Jujuy, Argentina