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Self‑Emergent Law Dynamics (SELD) in Complex Quantum Systems

Jincheng Zhang

Published Aug 19, 2026• 0 citations
Publisher

Abstract

In this paper we introduce a novel theoretical framework called Self‑Emergent Law Dynamics (SELD) that describes how local effective laws can arise spontaneously within large‑scale quantum systems. The central proposition of SELD is that the collective behavior of many interacting quantum degrees of freedom can give rise to emergent dynamical equations that are not evident in the microscopic Hamiltonian but become locally valid over certain spatial and temporal scales. We develop a mathematical description of SELD, define the local effective law L_eff(x), and discuss how quantum simulators can be employed to explore and validate these emergent phenomena. The potential breakthroughs of this approach include new insights into the emergence of classical physics from quantum mechanics, the design of adaptive quantum materials, and novel mechanisms for controlling quantum dynamics in engineered systems. By focusing on the dynamics rather than static properties, SELD opens a pathway to understanding how physical laws themselves may be dynamic, context‑dependent, and capable of self‑organization in complex quantum environments.

DOI
10.5281/zenodo.22005712

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Quantum many‑body systems exhibit a wealth of collective phenomena that cannot be inferred from the microscopic dynamics alone. In this work we introduce the concept of Self‑Emergent Law Dynamics (SELD) to describe how complex quantum systems spontaneously generate local effective laws that govern their own long‑time behavior. The central hypothesis is that, given a high‑dimensional Hilbert space and a Hamiltonian with local interactions, coarse‑graining over microscopic degrees of freedom can produce a position‑dependent effective Lagrangian L_eff(x) that captures the emergent dynamics of observable modes. We develop a theoretical framework to derive L_eff(x) from the underlying microscopic Hamiltonian, discuss the role of quantum entanglement and symmetry breaking, and propose experimental signatures that can be tested on quantum simulators. The paper outlines potential breakthroughs in understanding the emergence of physical laws, the design of self‑organized quantum devices, and new routes to simulate high‑energy physics phenomena.
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In many-body quantum systems, especially those with strong electronic correlations, the collective behavior of quasiparticles can give rise to emergent gauge degrees of freedom that are not imposed externally but generated intrinsically by the dynamics of the system. This paper proposes a unified theoretical framework for describing such self-generated gauge fields, here denoted as AμeffA_{\mu}^{\text{eff}}Aμeff​, that arise naturally in quantum matter. We formulate the conditions under which the internal degrees of freedom of a material can spontaneously form a gauge structure, and we derive the effective action for the emergent gauge field in terms of the microscopic variables. The formalism is applied to a variety of strongly correlated systems, including spin liquids, fractional quantum Hall states, and high-temperature superconductors, illustrating how AμeffA_{\mu}^{\text{eff}}Aμeff​ modifies the low-energy excitations and leads to novel observable phenomena. Furthermore, we discuss the potential of these emergent interactions to serve as platforms for discovering new artificial fundamental forces, thereby opening a route toward Nobel Prize–level physics.
This paper investigates the dynamic modeling of self-organized quantum entanglement, aiming to establish a framework for simulating quantum systems within complex environments. We propose a novel system model predicated on the unique properties of self-organized quantum entanglement, employing a combination of quantum mechanics and dynamical systems theory to simulate self-organization and analyze its emergent effects. The core claim is to develop a robust theoretical base for quantum information processing and quantum computation by providing a detailed simulation approach. The study will explore the fundamental characteristics of self-organized entanglement and its implications for designing effective quantum algorithms and information protocols. This work offers a significant advancement in our understanding of how to apply quantum mechanics to complex systems, providing a foundation for future research in quantum technologies.
The ontological status of physical laws remains one of the deepest inquiries in theoretical physics. This paper introduces the theoretical framework of the Spontaneous Law Selection Experiment (SLSE), investigating whether physical laws can emerge as stable dynamical attractors through complex system self-organization rather than acting as immutable external axioms. By constructing a generalized quantum simulator governed by a multi-branch superposition of candidate Hamiltonians expressed as H = sum_k p_k(t) H_k, we explore the conditions under which an evolving system spontaneously biases toward a specific effective dynamical regime where p_k(t) approaches 1 for a particular index k. We formalize the corresponding order parameters, symmetry-breaking mechanisms, Jacobian stability criteria, and information-theoretic bounds governing the thermodynamic costs of law selection. By shifting the perspective of physical laws from fundamental constraints to dynamically selected attractors, SLSE provides a robust conceptual foundation for understanding the origin of physical regularities in nature.
Complex quantum materials often exhibit unexpected emergent phenomena that cannot be fully explained by conventional band theory or mean-field approximations. In this paper, we propose that within the microscopic lattice of such materials a hidden causal network can self-organize. This causal network, represented by a matrix C_{ij}, captures directional dependencies between local degrees of freedom that influence electronic transport, spin dynamics, and energy redistribution. By formulating a set of coupled equations that relate the causal matrix to observable transport coefficients, we demonstrate that the causal structure can be inferred from macroscopic measurements. This framework provides a unifying perspective linking matter, information, and causality, and offers a potential pathway toward engineering quantum materials with tailored transport characteristics. The idea of self-generated causal structure may also shed light on the emergence of complex quantum behavior in strongly correlated systems and point toward future Nobel‑level discoveries in quantum materials science.