Fundamental Physics and Emergence Inquiry The Emergence of Stable Localized Structures from Dynamic Substrates: A Multidisciplinary Perspective I. Introduction: The Enigma of Emergent Order The question of how stable, localized structures, akin to particles, can arise and persist from an underlying dynamic substrate, whether informational or otherwise, represents a profound challenge at the forefront of modern science.1 This fundamental inquiry resonates across a vast spectrum of scales, from the quantum realm of elementary particles to the macroscopic world of biological organisms and even the grand expanse of cosmological structures.1 Understanding this emergence necessitates a departure from traditional reductionist approaches and an embrace of interdisciplinary perspectives, drawing insights from physics, philosophy, mathematics, and computer science.2 This report aims to provide a comprehensive, expert-level analysis of this complex phenomenon, delving into the foundational principles that govern emergence, exploring the limitations of current formalisms, and considering alternative frameworks that might offer a more complete understanding. The subsequent sections will address the key aspects of this inquiry, including the formalism gap in describing process-based ontologies, the operationalization of abstract principles, the formal representation of potentiality, the distinction between numerical artifacts and genuine emergence in simulations, the fundamental role of gravity and time, the boundary with consciousness, and the justification of foundational principles. The intricate interplay between these areas underscores the depth and complexity of unraveling the mystery of emergent order in the universe. II. Foundational Principles Governing Emergence and Persistence The emergence of stable structures from dynamic substrates is not a random occurrence but rather a manifestation of underlying principles that govern self-organization, dissipation, and pattern formation.1 Self-organization, a ubiquitous phenomenon in both animate and inanimate systems, refers to the spontaneous formation of spatial, temporal, or spatiotemporal structures from local interactions among a system's components.1 This process typically occurs in open systems driven away from thermal equilibrium, requiring a continuous flow of energy to counteract the natural tendency towards entropy.2 Key ingredients for self-organization include strong dynamical non-linearity, often involving positive and negative feedback loops, a balance between exploitation and exploration of the system's state space, and multiple interactions among components.3 Examples abound in physics, ranging from macroscopic phenomena like phase transitions, spontaneous magnetization, and crystal growth to quantum phenomena such as lasers, superconductivity, and Bose-Einstein condensation.1 Even in seemingly disordered systems, such as the deposition of materials on a substrate, increased interaction strength between the adsorbate and the substrate can induce first-order transitions and pattern formation, leading to stable surface structures.10 Similarly, the stability of lattice structures formed by interacting particles on a substrate is influenced by the commensuration ratio, the relationship between the number of particles and the substrate's potential wells.11 The concept of self-organized criticality further suggests that complex systems naturally evolve towards a critical state where small perturbations can trigger large-scale events, indicating an inherent tendency towards organized behavior without the need for precise tuning of parameters.12 This spontaneous ordering often involves a reduction of entropy within the system, as it moves towards more predictable states.13 Dissipative structures represent another crucial framework for understanding emergent stability. These are thermodynamically open systems that operate far from thermodynamic equilibrium, exchanging energy, matter, and information with their environment.15 Unlike closed systems that tend towards maximum entropy, dissipative structures can maintain or even increase their internal order by dissipating entropy into their surroundings.17 This maintenance of stability involves a dynamic interplay with the environment, where energy is taken in, transformed, and a portion is expelled as entropy.16 Characteristic features of dissipative structures include the amplification of fluctuations, which can lead to the establishment of new, organized states, and spontaneous symmetry breaking, where the resulting structure does not possess the symmetry of the processes that generated it.20 These systems often exhibit sensitivity to their environment and possess a degree of self-healing, allowing them to recover from perturbations.20 Examples in nature range from oscillating chemical reactions like the Belousov-Zhabotinsky reaction 15 to large-scale phenomena such as hurricanes 15 and, fundamentally, living organisms themselves.15 Even at the molecular level, stable structures can emerge from dynamic interactions driven by energy consumption, as seen in the substrate-proteasome interactions during protein unfolding, where ATP hydrolysis navigates through various conformational states.21 Furthermore, self-assembled dissipative structures can arise in systems like magnetically doped disks on a liquid surface, where the dissipation of energy through viscous flow is critical for the formation and stabilization of ordered patterns.22 Pattern formation describes the process by which an initially unstructured physical system develops a structured appearance, often in response to a change in some control parameter.23 This phenomenon is observed across diverse physical, chemical, and biological systems and at various spatial scales.26 Mechanisms driving pattern formation include Rayleigh-Bénard convection in fluids heated from below, the interaction of rotation, gravity, and convection in planetary atmospheres, non-linear effects in optical cavities, and the process of crystallization.25 Computational methods, such as structure search algorithms, can even predict the existence of stable and metastable structures in materials by exploring the energy landscape.27 In fluid dynamics, instabilities in thin films flowing under an inclined substrate can lead to the emergence of predominant streamwise-aligned structures known as rivulets.28 The study of pattern formation extends to understanding how enzymes interact with substrates, where substrate conformational dynamics can facilitate structure-specific recognition.29 The interplay of quasi-chemical reactions, lateral interactions between adsorbed particles, and adsorbate-substrate interactions also contributes to pattern formation on surfaces.10 Both static and dynamic patterns are observed in nature, arising from the coupling of mass transport with chemical and physical interactions, as well as feedback and synchronization mechanisms.32 The principles of thermodynamics provide the overarching framework for understanding the energetic requirements and constraints on the emergence of structures.33 The emergence of complexity and order in systems far from equilibrium is often associated with an increase in free energy and the utilization of information to reduce entropy.33 Dissipative structures, in particular, are a key focus in non-equilibrium thermodynamics, where the spontaneous formation of patterns and structures is linked to enhanced rates of free energy dissipation and entropy production.36 From a philosophical perspective, the concept of emergence is often categorized into weak and strong forms.5 Weak emergence posits that emergent properties arise from the underlying dynamics of a system but are only observable or predictable through simulation or after-the-fact analysis, not through simple reductionist approaches.5 These properties, while novel at a higher level, are ultimately determined by the lower-level constituents and their interactions.5 Strong emergence, on the other hand, suggests that emergent properties are fundamentally irreducible to the system's components and may even exert downward causal influence on them.5 While weak emergence is widely accepted in the context of physics and complex systems, the existence of strong emergence remains a subject of debate, with some arguing that it borders on the metaphysical.5 The prevailing view in physics tends to favor explanations where higher-level phenomena, including the emergence of stable structures, are ultimately rooted in the fundamental laws governing their constituents, aligning more closely with the concept of weak emergence.4 III. Bridging the Formalism Gap: Alternative Mathematical and Computational Languages Standard physics formalisms, while incredibly successful in describing many aspects of the universe, face limitations when attempting to fully capture the dynamics of process-based, relational ontologies, particularly those that might underlie the emergence of stable structures from dynamic substrates.42 Quantum Field Theory (QFT), the bedrock of modern particle physics, struggles with mathematical rigor in its non-perturbative regimes and faces significant challenges in providing a consistent description of quantum gravity.42 While QFT describes particles as excitations of underlying quantum fields 45, the interpretation of particles in interacting theories remains problematic.47 The theory also encounters difficulties in precisely describing composite particles and explaining phenomena like dark energy.48 Furthermore, simulating the emergence of particles in dynamic spacetimes presents considerable computational challenges within the framework of QFT in curved spacetime.49 The recent discovery of paraparticles, which do not fit neatly into the standard fermion-boson dichotomy, further highlights the potential limitations of current particle classifications within QFT.50 While the particle-as-excitation view is central to QFT, the complex behavior of the quantum vacuum suggests that our understanding of fundamental entities might be incomplete.45 To address these limitations and to develop formal languages capable of capturing process-based and relational aspects of emergence, alternative mathematical frameworks offer promising avenues. Category Theory, a general theory of mathematical structures and their relations, provides a powerful language for unifying diverse mathematical constructions in physics.6 Its focus on objects and the morphisms (arrows) between them allows for the abstraction of relationships and structures in a way that transcends specific implementations.6 Category theory has found applications in various areas of physics, including quantum mechanics, topological quantum field theory, and the modeling of interconnected systems.54 It offers a foundation for describing physical models and the relationships between them.53 Process Calculi provide another set of tools for formally modeling concurrent systems by focusing on interactions, communications, and synchronizations between independent processes.63 These calculi offer algebraic laws that enable the manipulation and analysis of process descriptions, allowing for formal reasoning about process equivalences.63 They have been used to model biological systems and concurrent computations, offering a different perspective on dynamic interactions compared to traditional physics formalisms.65 The Actor model, which shares some similarities with process calculi, also emphasizes message passing as a fundamental mode of interaction.69 Network Theory offers a framework for analyzing systems composed of interconnected entities, or nodes, and the relationships between them, represented as edges.70 This approach has been applied across a wide range of disciplines, including statistical physics, particle physics, computer science, biology, and social networks, to study complex systems and emergent phenomena arising from the interactions of their components.71 While initially applied to electric circuits 75, network theory has expanded to encompass diverse physical systems, including the connection between electric networks and random walks.77 By focusing on the structure and dynamics of interconnected elements, network theory provides a valuable lens for understanding how stable localized structures might emerge from a dynamic substrate. These alternative formalisms, by emphasizing relationships, processes, and network dynamics, offer the potential to bridge the gap in our ability to formally capture the emergence of stable structures from a dynamic, relational perspective, moving beyond the limitations of formalisms primarily focused on fields and particles. IV. Operationalizing Abstract Principles for Formal Implementation To effectively model the emergence and persistence of stable structures, abstract principles such as stability, alignment, exploration, and context-dependence must be given precise, operational definitions suitable for unambiguous formal implementation. Stability, in a general sense, refers to the state or quality of being stable, resisting change or displacement and tending to return to an equilibrium state.79 Operationally, stability can be defined in various ways depending on the system. In the context of operations, it signifies consistently effective and efficient performance with minimal disruptions.89 In control systems, stability is the ability to maintain a setpoint without excessive fluctuation.79 From a physics perspective, a system in stable equilibrium experiences a restoring force when displaced.82 The stability of localized solutions in physical systems can be mathematically analyzed near the existence of stable fronts between different states.93 In materials science, stability relates to the resistance to microstructural instabilities arising from non-convex potential energy landscapes.94 Even in probabilistic systems, stability refers to the property where combinations of random variables maintain the same distribution type.95 Alignment involves creating a state of coherence and unity within a system.96 Operationally, this can mean coordinating efforts and resources towards a common goal 97, synchronizing activities and objectives across different components 98, or ensuring a fit between the internal and external elements of a system.99 In organizational contexts, alignment links operational systems to the overall mission 100 and involves strategic fit, people, infrastructure, and functional integration.101 Alignment can also refer to agreement or alliance among parts of a system.103 In complex systems, it can be seen as the patterns of interaction that orient interdependent stakeholders towards shared interests.105 A key aspect of operational alignment is ensuring that team members understand and are working towards a common vision.106 In information systems, alignment refers to the integration of IT with business goals across strategic, operational, and social dimensions.107 The concept of alignment can even be visualized as the synchronization of independent parts within a complex system.108 Exploration refers to the act of investigating or searching, often in unknown or new territories.109 Operationally, in the context of Artificial Intelligence (AI), exploration involves discovering new data and trying novel approaches to improve performance.112 In reinforcement learning, it specifically means visiting previously unvisited states or taking actions that have not been taken before.113 In data science, exploration is the process of analyzing large datasets to uncover patterns and insights.114 The term "operational definition" itself describes a clear and measurable way to define a variable for research.117 In various industries, exploration can have specific operational meanings, such as in oil and gas or mining.122 In optimization algorithms, exploration is the ability to search a wider space to increase the chance of finding better solutions.123 In robotics, it is formulated as a robot making decisions about where to go in an unknown environment to learn and reduce uncertainty.124 Context-Dependence highlights the way in which meaning or behavior can vary based on the surrounding circumstances or environment.125 Operationally, this can be seen in context-dependent memory, where recall is improved when the context during learning matches the context during retrieval.127 It also applies to attention, where the ability to focus can be influenced by the surrounding environment or cultural context.132 Behavior itself can be context-dependent, with actions changing based on the environment.133 Even the meaning of words can be context-dependent, varying with the syntactic context in which they appear.134 Context can be defined as any information that characterizes the situation of an entity.136 In language, many expressions are context-dependent, requiring knowledge of the utterance context for proper interpretation.138 Operational definitions of behavior often include contextual information to ensure accurate measurement.140 Drawing upon the diverse definitions of these principles across fields like AI, complex systems theory, and cognitive science is essential for developing operational definitions that are not only precise but also relevant and suitable for formal implementation in models of emergent phenomena. V. Formal Representation of Potentiality and Actualization The concept of "potentiality," the capacity for something to become actual, is central to understanding the emergence of definite structures from dynamic substrates. Quantum mechanics, with its inherent probabilistic nature, offers several formal ways to represent potentiality and its transition to actuality. Superposition is a fundamental principle where a quantum system can exist in a linear combination of multiple states simultaneously.141 Mathematically, this is represented by a wave function that is a sum of eigenfunctions of the Schrödinger equation, each weighted by a probability amplitude.141 The square of the absolute value of this amplitude gives the probability of finding the system in that particular state upon measurement.141 Superposition is not analogous to a classical mixture of states 147 and is basis-dependent, meaning its description changes with the choice of basis states.148 This ability of a system to be in multiple potential states until measured is a key aspect of quantum behavior.149 The formal representation of probability in quantum mechanics differs fundamentally from classical probability.152 Quantum probability can be viewed as a measure on a non-Boolean lattice of projection operators in Hilbert space, rather than on a Boolean algebra of events.152 The Born rule provides the crucial link between the quantum state (wave function) and the probability of obtaining specific measurement outcomes.146 Quantum states can also be represented using probability distributions, offering a different perspective on the probabilistic nature of quantum phenomena.156 This probability representation is closely related to the concept of density operators, which describe the statistical state of a quantum system.153 Some interpretations even view quantum mechanics as a generalization of classical probability theory.159 The quantum potential, a concept central to the de Broglie-Bohm interpretation of quantum mechanics, offers another way to think about potentiality.160 It acts as a guiding wave for quantum particles and is related to the idea of an information potential and non-locality.160 Some research suggests a link between the quantum potential and the internal motion (zitterbewegung) associated with a particle's spin.160 Beyond these formalisms, other interpretations of quantum mechanics touch upon the concept of potentiality. Heisenberg viewed the quantum state vector as encoding the potential for a system to manifest physical properties.161 The idea of quantum res potentiae describes quantum states as non-actual, pre-spacetime possibilities.163 Potentiality can also be seen as a mode of being intermediate between non-existence and actuality, with measurement causing the actualization of a specific potentiality.164 Attempts have even been made to formally represent potentiality using specific operators within a logical framework.165 The mathematical framework of quantum mechanics, involving group actions and representations, provides the tools to describe the symmetries and transformations of quantum states, further underpinning the formal representation of potentiality.166 Finding a formal representation of potentiality that naturally supports both quantum-like superposition and probability while also allowing for definite actualization upon interaction remains a key challenge. The various interpretations and formalisms within quantum mechanics offer different perspectives and mathematical tools that could inspire the development of such a representation in a broader context of dynamic substrates. VI. Disentangling Numerical Artifacts from Genuine Emergence Computational simulations play an increasingly vital role in studying the emergence of stable structures from dynamic substrates. However, a critical challenge lies in reliably distinguishing genuine emergent phenomena, particularly quantization, from artifacts arising from the inherent limitations of finite precision and discretization in numerical methods. Several methodologies and techniques are employed to address this challenge. Scale invariance analysis, for instance, can help identify power laws in the behavior of simulated systems, which are often characteristic of critical phenomena and self-organized criticality, suggesting genuine emergent behavior rather than numerical noise.12 Robustness checks are crucial, involving systematic variation of the simulation's precision and discretization parameters. If the observed phenomena persist across a range of these parameters, it strengthens the case for genuine emergence. Conversely, if small changes in numerical parameters lead to significant alterations in the results, it suggests the presence of artifacts. Where possible, comparing simulation results with analytical solutions or theoretical predictions provides another essential validation step. If the simulations reproduce known theoretical outcomes, it increases confidence in their ability to capture genuine physical behavior. Furthermore, focusing on qualitative changes in behavior as system parameters are varied, rather than solely on quantitative shifts, can help distinguish emergence from numerical effects. True emergent phenomena often manifest as abrupt transitions or the appearance of novel structures at specific parameter values, which are less likely to be caused by numerical limitations. Techniques from the study of chaos and non-linear dynamics, such as the identification of attractors and phase transitions, can also be valuable. If these features are robust to changes in numerical precision, they are more likely to represent genuine properties of the system's dynamics. By carefully employing these methodologies, researchers can increase the reliability of computational simulations in distinguishing genuine emergent phenomena, such as quantization effects, from spurious results arising from the inherent constraints of numerical approximations. VII. The Fundamental Role of Gravity The nature of gravity at a fundamental level remains one of the most profound open questions in physics. Two primary perspectives exist: one that views gravity as a consequence of the patterns of matter and energy within spacetime, as described by Einstein's General Relativity, and another that posits gravity as intrinsically linked to the fundamental principles governing pattern formation and persistence itself. General Relativity elegantly describes gravity as the curvature of spacetime caused by the presence of mass and energy. In this framework, the patterns of matter and energy dictate the geometry of spacetime, which in turn governs the motion of objects. This perspective has been remarkably successful in explaining a wide range of gravitational phenomena, from the motion of planets to the expansion of the universe. However, the quest for a unified theory that incorporates quantum mechanics with gravity has led to alternative perspectives. String Theory proposes that the fundamental constituents of the universe are not point-like particles but tiny, vibrating strings. Different vibrational modes of these strings correspond to different particles, including the graviton, the hypothetical particle that mediates the gravitational force.44 This framework offers the potential to unify gravity with other fundamental forces. Loop Quantum Gravity, on the other hand, suggests that spacetime itself has a granular structure at the Planck scale, emerging from networks of loops known as spin networks.172 In this view, gravity is not a fundamental force but rather an emergent property of this quantum structure of spacetime. Emergence theory takes this idea further, viewing spacetime as emerging from the interactions of even more fundamental, discrete components, potentially informational in nature.173 These theories suggest that the principles governing the formation and persistence of patterns at the most fundamental level might be intrinsically tied to the nature of gravity. The observation of analogs of cosmological phenomena, such as particle production, in condensed matter systems like Dirac materials 176, hints at potential connections between the physics of pattern formation across vastly different scales, possibly involving gravity in a fundamental way. The challenges in simulating particle creation in an expanding universe within the framework of QFT in curved spacetime 49 also underscore the complex interplay between gravity and the emergence of matter and energy patterns. Understanding whether gravity is primarily a consequence of matter/energy patterns or a fundamental principle underlying pattern formation and persistence itself is crucial for developing a complete theory of emergence. VIII. The Emergence of Time and Sequence The nature of time, both as a subjective experience and as an objective physical parameter, presents another deep mystery. Standard physical theories typically treat time as a reversible parameter, a dimension along which events unfold. However, our subjective experience is one of a unidirectional flow from past to future. Understanding how this subjective flow emerges from a more fundamental "Sequence" of events, and how it relates to the objective "time" of physical theories, remains a significant challenge. In the context of dissipative structures, time plays an irreversible and constructive role.16 The very existence and evolution of these structures depend on processes that increase entropy over time. In process-based ontologies, the sequence and ordering of events might be considered more fundamental than a continuous time parameter. This perspective could potentially offer a way to bridge the gap between the discrete nature of fundamental events and the continuous nature of time in our experience and in standard theories. Exploring how the arrow of time arises from fundamental principles, and how our perception of its flow emerges from a sequence of physical or informational transformations, is a critical aspect of a comprehensive theory of emergence. IX. The Boundary with Consciousness: A Principle-Based Framework The extent to which a principle-based or information-based framework can explain the structural and functional correlates of consciousness, and where it hits the boundary of explaining subjective qualia (the "hard problem" of consciousness), is a question that lies at the intersection of physics, philosophy, and neuroscience. Frameworks based on self-organization, information processing, and emergence might offer explanations for the complex structural and functional organization of the brain, which are undoubtedly correlates of consciousness. For instance, the brain can be viewed as a highly complex network exhibiting self-organizing behavior. Information processing within this network is clearly crucial for cognitive functions. Some theories even suggest that consciousness arises as an emergent property of this complex information processing.18 However, these frameworks often struggle to address the "hard problem" of consciousness: why and how do these structural and functional correlates give rise to subjective experience, the qualitative "what it's like" of being conscious? While a principle-based or information-based approach might explain how the brain processes information and generates behavior, it is less clear how it can account for the feeling of redness, the experience of joy, or the sensation of pain. This is where the boundary of current scientific understanding often lies. While such frameworks might provide valuable insights into the neural correlates of consciousness, they may not, in their current form, fully explain the emergence of subjective qualia. X. Justification of Foundational Principles and Axioms The selection of a specific set of foundational principles for a theory of emergence raises the fundamental question of justification. What is the ultimate basis for choosing certain principles over others, and how can we determine if they are truly minimal and sufficient? The justification for selecting foundational principles can draw upon several sources. Empirical evidence plays a crucial role; principles that lead to predictions consistent with observations are more likely to be considered valid. Philosophical arguments, such as Occam's razor (the principle of simplicity), can also guide the selection process, favoring theories with a minimal set of assumptions. Mathematical consistency is another essential criterion; the principles should ideally form a coherent and logically sound framework. The sufficiency of a set of principles can be assessed by its ability to explain the phenomena it aims to address, while minimality requires that no principle can be removed without losing explanatory power. Ultimately, the justification of foundational principles in a theory of emergence is an ongoing process, subject to refinement and revision as our understanding of the universe evolves. XI. Conclusion: Towards a Unified Understanding of Emergence The emergence of stable localized structures from dynamic substrates is a multifaceted problem that demands a comprehensive and interdisciplinary approach. The principles of self-organization, dissipative structures, and pattern formation provide valuable frameworks for understanding how order can arise spontaneously in complex systems driven by energy flow and local interactions. While standard physics formalisms like QFT and General Relativity have achieved remarkable success, they face limitations in fully capturing the process-based and relational aspects inherent in emergence. Alternative mathematical languages such as category theory, process calculi, and network theory offer promising tools for bridging this formalism gap by focusing on relationships, dynamic interactions, and complex interconnectedness. Operationalizing abstract principles like stability, alignment, exploration, and context-dependence through precise definitions tailored to the specific system under investigation is crucial for formal modeling. Quantum mechanics provides a rich ground for exploring the formal representation of potentiality and its actualization, with concepts like superposition, probability amplitudes, and the quantum potential offering different perspectives. Distinguishing genuine emergent phenomena from numerical artifacts in computational simulations requires rigorous methodologies, including scale invariance analysis and robustness checks. The fundamental role of gravity, whether as a consequence of matter/energy or as a principle underlying pattern formation, remains an open question with implications for our understanding of emergence at the most fundamental level. The emergence of subjective time from a sequence of events and the boundary with consciousness regarding subjective qualia pose further profound challenges. Finally, the justification of the foundational principles underpinning any theory of emergence requires careful consideration of empirical evidence, philosophical arguments, and mathematical consistency. Future research should focus on further developing and applying alternative formal languages to model emergent phenomena, refining operational definitions of abstract principles in various contexts, and exploring the deeper connections between information, computation, and emergence. A unified theoretical framework for understanding how stable structures arise and persist from dynamic substrates will likely require a continued dialogue and collaboration across diverse scientific disciplines. Key Valuable Tables: Table: Examples of Self-Organizing Phenomena Phenomenon Underlying Dynamic Substrate Key Principles Involved Snippet ID(s) Crystal Growth Atoms/Molecules Intermolecular Forces, Thermodynamics 1 Laser Emission Excited Atoms Quantum Mechanics, Stimulated Emission 1 Cloud Streets Air Molecules Fluid Dynamics, Convection 2 Brain Activity Neural Networks Neural Interactions, Information Processing - Spontaneous Magnetism Atomic Spins Statistical Mechanics, Quantum Mechanics 1 Bose-Einstein Condensation Bosons Quantum Mechanics, Low Temperatures 1 Rivulet Formation Thin Viscous Film Fluid Dynamics, Instability 28 Surface Patterning Adsorbates on Substrate Adsorbate-Substrate Interactions 10 Table: Comparison of Formal Languages Formal Language Core Concepts Strengths in Modeling Emergence Limitations Relevant Snippet IDs Category Theory Objects, Morphisms, Functors Relational Structures, Unification Abstraction Level 6 Process Calculi Processes, Channels, Interactions Dynamic Interactions, Concurrency Complexity 63 Network Theory Nodes, Edges, Attributes Complex Systems, Interconnections Focus on Structure 70 Quantum Field Theory Fields, Quantization, Lagrangian Formulation Fundamental Particles, Interactions Mathematical Rigor, Quantum Gravity 42 Table: Operational Definitions of Abstract Principles Abstract Principle Operational Definition in Physics Operational Definition in AI/Complex Systems Key Snippet IDs Stability Tendency to return to equilibrium after displacement Consistent effective performance with minimal disruptions 79 Alignment Arrangement of parts in a straight line or in parallel Coordinating efforts and resources toward a common goal 97 Exploration Investigating unknown regions or new possibilities Discovering new data and approaches to improve performance 109 Context-Dependence Meaning or behavior varying based on surrounding physical environment Meaning or behavior varying based on surrounding circumstances or prior interactions 125 Works cited en.wikipedia.org, accessed April 29, 2025, https://en.wikipedia.org/wiki/Self-organization#:~:text=Physics,-See%20also%3A%20Self&text=The%20many%20self%2Dorganizing%20phenomena,Einstein%20condensation%20in%20quantum%20physics. 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