Abstract This paper supplements existing descriptions of quantum physics at the phenomenological level by proposing a continuous dynamical model based on Information-Structured Effective Fields (ISEF). The core of this work is to establish the Fisher information density functional as the fundamental driving source for the evolution of the system state. By applying a variational treatment to this information functional, the framework shows, without introducing additional microscopic ontological assumptions, how the inhomogeneity of the probability density (ρ) manifests as an intrinsic structural tension, from which the trend potential (Φ_trend) governing the dynamics can be derived. Starting from this Fisher-information-driven chain, the paper derives a rigorous coupling map between the density distribution ρ and the evolving phase parameter ω. This mechanism is expected to provide a logically self-consistent and unified continuous phenomenological explanation for double-slit interference, the coherence decay caused by path-information acquisition, and the statistical decoherence of massive complex systems such as C₆₀ molecules. This work demonstrates the fundamental role of the Fisher information functional in constraining and driving the evolution of physical systems, and it also provides theoretical expectations for the macroscopic decoherence boundary of matter-wave interference that can be tested in future experiments.
Abstract This paper supplements existing descriptions of quantum physics at the phenomenological level by proposing a continuous dynamical model based on Information-Structured Effective Fields (ISEF). The core of this work is to establish the Fisher information density functional as the fundamental driving source for the evolution of the system state. By applying a variational treatment to this information functional, the framework shows, without introducing additional microscopic ontological assumptions, how the inhomogeneity of the probability density (ρ) manifests as an intrinsic structural tension, from which the trend potential (Φ_trend) governing the dynamics can be derived. Starting from this Fisher-information-driven chain, the paper derives a rigorous coupling map between the density distribution ρ and the evolving phase parameter ω. This mechanism is expected to provide a logically self-consistent and unified continuous phenomenological explanation for double-slit interference, the coherence decay caused by path-information acquisition, and the statistical decoherence of massive complex systems such as C₆₀ molecules. This work demonstrates the fundamental role of the Fisher information functional in constraining and driving the evolution of physical systems, and it also provides theoretical expectations for the macroscopic decoherence boundary of matter-wave interference that can be tested in future experiments.
Based on open quantum systems and non-equilibrium field dynamics, a unified physical theory connecting cosmic evolution and microscopic quantum decoherence is established. Two core axioms are proposed: the non-equilibrium field difference axiom provides the external rigid condition for the emergence of ordered structures, and the quantum intrinsic upward chemotaxis axiom describes the internal driving force for systems to evolve toward higher information integration and complexity. Using an ultra-low temperature global field and a local ordered microenvironment as an analog model, the underlying isomorphic logic of cosmic and life evolution is revealed. The theory is embedded into the open quantum system framework, and the intrinsic chemotaxis correction is introduced into the standard Lindblad master equation to construct a full quantum master equation at the density matrix level. The time-dependent effective decoherence rate Γₑբբ(t)=Γ−βαe⁻ᵅᵗ is rigorously derived, and the analytical solution of coherence decay C(t)=exp(−Γt+β(1−e⁻ᵅᵗ)) is obtained. The theory predicts that quantum coherence exhibits non-exponential stretched decay under ultra-low temperature and low noise conditions, which is falsifiably different from the mainstream pure exponential decay. The physical definitions and theoretical constraints of parameters β and α are clarified, and a semi-quantitative magnitude estimate is given (optimistic upper bound β≲10⁻⁶, to be determined experimentally). Four groups of controlled experiments are designed based on platforms such as superconducting qubits and ion traps, and four quantitative test criteria are proposed to evaluate the experimental feasibility. This theory defines the second law of thermodynamics as an effective law for macroscopic isolated systems, establishes intrinsic chemotaxis as the core driving force for directed evolution, and forms a complete logical closed-loop from unified physical framework and cosmic evolution model to microscopic experimental predictions.
A mathematically explicit extension of quantum hydrodynamics is developed in which a scalar coherence field ΦG modifies phase transport and is driven by the information-geometric structure of the probability density together with probability transport itself. The construction starts from the Madelung representation Ψ = √ρ eiS/ℏ, augments the phase gradient by the covariant shift ∇S ↦ ∇S − αℏ∇ΦG, and defines the dynamics through a variational (ρ, S) sector together with a dissipative Onsager-type relaxation law for ΦG. This yields a closed PDE system consisting of a continuity equation, a modified Hamilton–Jacobi equation, and a coherence-field equation that reduces in the overdamped limit to an elliptic closure. The source of ΦG is neither bare mass density nor bare probability density: it is a local Fisher-information density together with probability transport, so that ΦG measures coherence demand. The field equations are written explicitly; the coupling sign is fixed by an energy-stability argument, the transport-forcing sign by a dissipation argument, and the induced coherence-pressure term is computed exactly. A structural no-signalling condition is obtained by restricting the nonlinearity to Fisher-marginal source functionals that are blind to the entanglement Fisher excess under marginalisation. A coarse-grained Yukawa sector is shown to admit a conditional Newtonian limit under explicitly stated screening and additivity assumptions; this remains a conjectural macroscopic regime rather than a completed derivation of gravity. The paper closes with a falsifiable numerical programme—ablation studies, dispersion diagnostics, Fisher-information monitoring, and an explicit pilot solver scaffold—together with a claim-status ledger, a testability map, and a development roadmap that separate what is defined, what is derived, what is heuristic, and what remains unproven. Keywords: quantum hydrodynamics; Fisher–Rao geometry; Madelung dynamics; coherence field; no-signalling; information geometry.
The hypothesis that physical information is not fundamentally destroyed motivates a mathematical question: can localization, correlation, and effective interaction be generated from an information-based variational principle without inserting the desired interaction potential by hand? We investigate this question in a framework built on the classical Fisher information of probability densities, organized around a strict anti-circularity requirement: no Coulomb kernel, inverse-distance potential, or prescribed interaction law is introduced into the fundamental functional. Several results are established at increasing levels of generality. First, under normalization and a fixed second moment, the Fisher information obeys the sharp bound I[ρ]≥d2/R2I[ρ]≥d2/R2, with equality attained uniquely by the isotropic Gaussian; this solves the one-body constrained problem completely. Second, for any joint density ρ12ρ12 with prescribed marginals, I12[ρ12]≥I[ρ1]+I[ρ2]I12[ρ12]≥I[ρ1]+I[ρ2], with equality attained by the product density; consequently a purely local, block-additive Fisher functional cannot generate an effective interaction at any separation, Keff(R)≡0Keff(R)≡0. Third, this no-go result is shown to be far more robust than the local case alone suggests: for any hidden-variable extension Q(x1,x2,z)Q(x1,x2,z) of a two-body density, ∀ Q(x1,x2,z):I[Q] ≥ I[ρ12] ≥ I[ρ1]+I[ρ2],∀Q(x1,x2,z):I[Q] ≥ I[ρ12] ≥ I[ρ1]+I[ρ2], unconditionally, with no independence, factorization, or weak-coupling assumption placed on the auxiliary variable zz, provided the enlarged functional remains the Fisher information of the enlarged density; no claim is made about enlargements governed by an arbitrary non-Fisher coupling of zz. Within that scope, this closes off an entire class of hidden-variable evasions of the no-go theorem at once, rather than ruling out evasions one construction at a time -- a consequence obtained by combining the superadditivity of Fisher information under marginalization, established by Carlen, with a further marginalization over the auxiliary sector; the contribution of this article is the variational reading of that combination as a no-interaction obstruction, together with an exact conditional-variance identity sharpening its equality case, rather than the underlying information inequality itself. We further characterize equality in the first marginalization step: equality of the full Fisher informations forces the auxiliary sector to factorize and to carry zero Fisher information, so on an unbounded connected auxiliary domain the equality case is impossible for a proper normalized density. We then show, with an explicit lower-bound hypothesis made a formal part of the statement rather than left implicit, that exact vanishing of KeffKeff follows whenever the auxiliary extension is block-factorized across the two subsystems, the governing functional contains no explicit cross-sector coupling term prior to elimination, and the functional obeys a block-additive lower bound over the entire admissible class (not merely on factorized configurations); the Fisher bound supplies this hypothesis automatically in the Fisher case. Conversely, Keff≠0Keff=0 implies that no admissible block-factorized configuration can realize the independent optimum, though the converse implication does not hold without further hypotheses. We then exhibit a concrete construction that violates factorization: an auxiliary scalar field sourced jointly by both subsystems. The functional E[ϕ,ρ]=κ2∫∣∇ϕ∣2−g∫sρϕE[ϕ,ρ]=2κ∫∣∇ϕ∣2−g∫sρϕ produces, after eliminating ϕϕ, a nonlocal quadratic functional with the Green kernel of the Laplacian, yielding a 1/R1/R interaction in three dimensions. We show carefully that this mechanism is not explained by the nonlocality of the map ρ↦ϕρ↦ϕ: a model with two independent, equally nonlocal fields remains sector-separable, and we verify directly (rather than by importing the Fisher-specific bound into a classical field functional, where it does not automatically apply) that its infimum splits additively, giving Keff≡0Keff≡0. The operative property behind the nonzero result is instead that a single shared field is sourced by the total density, which forces a cross term ∫∇ϕA⋅∇ϕB∫∇ϕA⋅∇ϕB absent from any factorized configuration. This mechanism reaches only the third of four levels in an anti-circularity hierarchy that we introduce; whether the field itself can be derived, rather than postulated, from an information-theoretic principle remains open. The resulting framework separates four logically distinct conclusions: a proved localization theorem, a proved no-interaction theorem for local Fisher information, an unconditional lower bound ruling out entire classes of hidden-variable evasions, and a concrete non-factorized extension whose physical interpretation and information-theoretic origin remain to be established. We close by fixing this boundary precisely and organizing the remaining program around a single unresolved question — whether a non-factorized shared mediator can itself be derived from an information-theoretic principle, rather than postulated — so that the present results are used as a fixed starting constraint on that question rather than reopened by it.
This work develops Dynamical Informational Field Theory (DIFT), a field-theoretic framework in which physical observables emerge from admissible, low-impedance organizations of an underlying scalar–phase field rather than from fundamental particles or external measurement postulates. The paper introduces admissibility pathways as variational selection mechanisms connecting the full informational field to the observable sectors of quantum mechanics and the Standard Model. The framework derives Born weights, interference, current closure, and effective unitarity as consequences of dynamostatic organization and boundary memory. Measurement is interpreted as boundary-induced phase closure under finite impedance rather than as an independent collapse axiom. Numerical evidence includes scalar–phase simulations of double-slit interference, which-path decoherence, admissibility-edge dynamics, and toroidal organizational pathways relevant to nuclear emergence. The manuscript combines formal derivations, controlled numerical validations, and a systematic correspondence map between standard physical concepts and their DIFT interpretations, providing a unified admissibility-based ontology for quantum phenomena.
This work develops a Lorentz-invariant variational framework in which Fisher-information geometry appears as an intrinsic structural contribution to quantum dynamics. Motivated by longstanding attempts to connect quantum mechanics with information-theoretic principles, we introduce an action functional depending on the density and phase fields in the Madelung representation. Variation of this action yields a modified Klein–Gordon equation containing a single nonlinear term proportional to the four-dimensional Fisher-information curvature of the probability density. The standard Klein–Gordon equation is recovered when the structural parameter vanishes, ensuring full compatibility with established relativistic dynamics. Taking the nonrelativistic limit, we obtain a uniquely determined nonlinear Schrödinger equation in which the correction term is the functional derivative of the Fisher information. The resulting dynamics preserve probability, maintain the Hamilton–Jacobi correspondence, and contain the linear Schrödinger equation as a special case. Analytical expressions for Gaussian and superposed states demonstrate how the structural modification scales with spatial localization and interference structure, providing clear qualitative signatures that distinguish the model from previous nonlinear extensions and offer a theoretical basis for future experimental verification. The results establish a mathematically transparent link between information geometry and quantum dynamics and provide a foundation for future extensions to fermionic, gauge, and many-body systems.
This paper presents a first-principles physical simulation of the double-slit experiment to investigate causal emergence in quantum systems. Unlike traditional approaches that rely on pre-sampled distributions, our simulation generates particle trajectories from fundamental physical laws, incorporating quantum interference potential and decoherence effects. We demonstrate that quantum coherence leads to causal emergence, where macroscopic descriptions contain more information than microscopic ones, as quantified by effective information (EI). The simulation reveals a phase transition at a critical decoherence strength, beyond which causal emergence disappears. Our results provide computational evidence for the theoretical framework of causal emergence in quantum mechanics and highlight the role of observation in altering explanatory power. The methodology avoids data filtering bias by generating trajectories self-consistently from physical principles.