Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Spin as Antisymmetric Transport: A Unified Entropic--Network Synthesis of Berry Phase, Pauli, Dirac, Chern--Simons, and Generalized Network Structures: Emergent Spin and Quantum Dynamics from Entropic Network Holonomy

fredrick michael

Published Mar 24, 2026• 0 citations
Publisher

Abstract

We develop a unified framework in which spin, quantum phase, and complex-valued dynamics arise from entropy-driven transport on generalized networks. Starting from a nonadditive entropy functional, we construct nonlinear transport operators whose noncommutativity emerges at the level of discrete network evolution. We show that transport around closed loops defines a holonomy, whose continuum limit yields an antisymmetric entropy curvature tensor. This curvature generates local rotational structure satisfying $J^2 = -I$, providing a geometric origin for complex numbers and quantum phase. In this formulation, the imaginary unit is not introduced as a postulate, but arises as the minimal representation of entropy-induced rotations. Linearizing the transport dynamics near equilibrium yields an effective Schr\"odinger equation, with the quantum of action determined by the strength of entropy curvature. We further demonstrate that the entropy tensor decomposes into symmetric and antisymmetric components corresponding, respectively, to spacetime geometry and quantum structure. This provides a unified description in which metric geometry and spin/phase phenomena emerge from a common entropic origin. Multiple physical frameworks—including Pauli and Dirac spin, Berry phase, Chern--Simons theory, and quantum Hall systems—are shown to correspond to representations of this underlying antisymmetric transport. This approach replaces the need for ad hoc analytic continuation or imposed complex structure, instead deriving quantum dynamics from noncommuting entropy transport. The results suggest a general connection between nonextensive entropy, holonomy, and quantum behavior, with potential implications for strongly correlated and non-equilibrium systems.

DOI
10.5281/zenodo.19209948

Related papers

Quantum Mechanics as Real Geometry: Curvature, Torsion, and Holonomy

Kwon, Se Kyun

While the complex formalism of quantum mechanics has been extraordinarily successful, the fundamental geometric origin of its core elements—the imaginary unit, operator non-commutativity, quantum phase, and the intrinsic geometry with quantum spin—has remained unresolved for more than a century. Here we resolve these foundational questions by deriving an exact and physically equivalent formulation of the Schrödinger equation as a Real Geometric Flow—a moving-frame evolution on a 2𝑁-dimensional real state space. In this restored framework, the global imaginary unit 𝑖 fully decomposes into a set of local skew-symmetric generators that drive planar rotations in real space, revealing that the traditional complex formalism is a compressed representation of an intrinsic rotational geometry.Within the real geometric flow, energy eigenvalues appear as the Curvatures of the state trajectory, energy gaps correspond to Torsions that couple internal planes—naturally generating the geometry of quantum spin—and quantum phase emerges naturally as the Holonomy of the real moving frame. This formulation preserves the full empirical content of quantum mechanics while exposing the geometric mechanisms hidden beneath its notation, providing the first coherent explanation of curvature, torsion, non-commutativity, spin behavior, and quantum phase within a single framework.By demonstrating that the algebraic postulates of quantum mechanics arise from a deeper geometric order—one that stands alongside curvature-based theories such as General Relativity—this work establishes a unified differential-geometric foundation for quantum dynamics.It opens new directions for quantum control, quantum information, and fundamental physics.

•Nov 24, 2025•0 citations

Exploring Boundary-Defects as Proposed Origins of Complex Quantum Dynamics: A Sequential Mechanics from Eulerian--Lagrangian Transport, Dirichlet--Neumann--Robin Structure, Holonomy, and Bell Correlations

fredrick michael

We develop a real-variable mechanics in which complex quantum dynamics is not postulated at the microscopic starting point. The central observation is that integration by parts does more than generate formal boundary terms: in a medium with defects, interfaces, punctures, grains, or excised sets, those boundary terms encode the admissible transport law. Dirichlet, Neumann, and Robin boundary conditions therefore become dynamical selectors for absorption, reflection, and partial reflection-reaction. Robin structure is especially important because the same boundary parameter controls boundary local time in diffusion and a momentum-dependent reflection phase in wave mechanics. We combine this with an Eulerian--Lagrangian description of transport, a symmetric/antisymmetric tensor decomposition, and a compatible antisymmetric two-form. On an oriented two-plane the normalized antisymmetric transport operator satisfies J^2=-I, furnishing a real complex structure without inserting the scalar 'i' by hand. Nelson-type forward/backward stochastic kinematics then produces the continuity equation, quantum potential, and Schrodinger form, while closed defect loops yield Berry-like holonomy. A Glauber master-equation route supplies a discrete stochastic precursor. Bell correlations are treated as an endpoint test of globally prepared nonseparable transport: Bell's theorem is retained in full, so the construction is not a Bell-local hidden-variable model. Rather, it proposes that local propagation can coexist with a globally prepared holonomy/correlation state whose measurement statistics need not factorize. Finally, we connect the symmetric transport sector to emergent 3-geometry, entanglement-area structure, and loop-quantum-gravity-style geometric observables. The paper separates established mathematics from the proposed synthesis and lists numerical and experimental falsification tests.

•Aug 24, 2026•0 citations

Phase-Connection Geometry and Non-Abelian Time Transport: A Curvature-Based Mechanism for Classicalization and Phase Dynamics

BORA AKTAŞ

Abstract We introduce a phase-geometric framework in which time evolution is governed by a covariant derivative defined over a multi-carrier phase space. The associated connection induces a non-abelian curvature whose holonomy generates measurable phase-transport effects. Within this unified geometric setting, the quantum–classical transition, phase-channel mixing, and time-transport anomalies arise from a single underlying mechanism. In contrast to conventional approaches, where gauge structures are imposed externally, the connection emerges intrinsically from the phase geometry itself. The framework yields calculable thresholds for classicalization and leads to novel, testable predictions based on curvature-induced phase holonomy.

•Jan 1, 2026•0 citations

From Diffusion to Quantum Mechanics via Haar Symmetry and Curvature

fredrick michael

We develop a unified framework in which quantum mechanics is assumed to emerge from combinatorial configuration spaces under evolution, curvature, and symmetry constraints. Starting from general discrete configurations such as permutations, tilings, and causal sets, we show that entropy and statistical ensembles arise naturally from counting arguments. Dynamical evolution leads to diffusion and irreversible behavior, while the presence of defects and holonomy introduces geometric phase structure. We demonstrate that invariance under compact symmetry groups, enforced via Haar measure, necessitates a transition from probabilities to amplitudes, yielding unitary and time-reversal symmetric dynamics. This provides a possible derivation of quantum mechanics from combinatorial and geometric principles, with applications to transport theory, nonequilibrium systems, and emergent spacetime.

•Mar 18, 2026•0 citations

Covariant formulation of the Berry connection in non-Hermitian systems

Ievgen I. Arkhipov

Non-Hermitian systems exhibit spectral and topological phenomena absent in Hermitian physics; however, their geometric characterization remains subtle due to the intrinsic ambiguity of biorthogonal eigenspaces. Since left and right eigenvectors are not related by Hermitian conjugation, the associated Berry connection is generally nonunique, leading to complex geometric phases and ambiguously defined holonomies. Here we formulate a covariant geometric framework for non-Hermitian quantum systems based on the metric structure of the underlying Hilbert space. We show that, in the quantum regime with continuous state evolution, the conventional Berry connection and the associated Berry holonomy over closed parameter-space loops can be consistently defined only in the pseudo-Hermitian limit, where the spectrum is real. For generic non-Hermitian Hamiltonians with complex spectra, the relevant geometric object is instead the Aharonov--Anandan holonomy associated with cyclic evolution in projective Hilbert space. Within the pseudo-Hermitian regime, we construct a unique Hermitian Berry connection that is covariant under arbitrary ${\rm GL}(N,\mathbb C)$ frame transformations and reduces to the standard Berry connection in the Hermitian limit. The resulting formalism separates the intrinsic geometry of the Hamiltonian eigenspace from contributions arising from the parameter dependence of the Hilbert-space metric, revealing that the conventional biorthogonal formulation generally mixes these distinct geometric effects. Consequently, geometric phases, synthetic gauge fields, and topological characteristics commonly attributed to non-Hermitian eigenspace geometry may, in part, originate from the underlying metric structure. Our framework therefore provides a consistent geometric foundation for Berry phases, non-Abelian holonomies, and topological invariants in non-Hermitian quantum systems.

quant-pharXiv:2601.19777•Physical Review Research•Jan 28, 2026•0 citations

An Operator–Entropic Framework for Emergent Quantum, Gauge, and Gravitational Dynamics

Borros Arneth

We propose a unified framework in which quantum dynamics, gauge interactions, and gravitational behavior arise from a common operator-based microscopic structure. The approach is based on a complex operator composed of two Hermitian components whose non-commutativity generates interaction effects. A positive density operator is constructed, and entropy is used as a central organizing principle connecting microscopic and macroscopic physics. Under general assumptions, the formalism reproduces unitary quantum evolution, provides a mechanism for the emergence of gauge structure, and connects entropy variation to gravitational dynamics. The framework is illustrated through an explicit solvable model demonstrating how interaction strength influences thermodynamic behavior. This work establishes a concrete mathematical basis for exploring a unified origin of fundamental interactions.

•Apr 14, 2026•0 citations
We develop a unified framework in which spin, quantum phase, and complex-valued dynamics arise from entropy-driven transport on generalized networks. Starting from a nonadditive entropy functional, we construct nonlinear transport operators whose noncommutativity emerges at the level of discrete network evolution. We show that transport around closed loops defines a holonomy, whose continuum limit yields an antisymmetric entropy curvature tensor. This curvature generates local rotational structure satisfying J2=−IJ^2 = -IJ2=−I, providing a geometric origin for complex numbers and quantum phase. In this formulation, the imaginary unit is not introduced as a postulate, but arises as the minimal representation of entropy-induced rotations. Linearizing the transport dynamics near equilibrium yields an effective Schr"odinger equation, with the quantum of action determined by the strength of entropy curvature. We further demonstrate that the entropy tensor decomposes into symmetric and antisymmetric components corresponding, respectively, to spacetime geometry and quantum structure. This provides a unified description in which metric geometry and spin/phase phenomena emerge from a common entropic origin. Multiple physical frameworks—including Pauli and Dirac spin, Berry phase, Chern--Simons theory, and quantum Hall systems—are shown to correspond to representations of this underlying antisymmetric transport. This approach replaces the need for ad hoc analytic continuation or imposed complex structure, instead deriving quantum dynamics from noncommuting entropy transport. The results suggest a general connection between nonextensive entropy, holonomy, and quantum behavior, with potential implications for strongly correlated and non-equilibrium systems.
While the complex formalism of quantum mechanics has been extraordinarily successful, the fundamental geometric origin of its core elements—the imaginary unit, operator non-commutativity, quantum phase, and the intrinsic geometry with quantum spin—has remained unresolved for more than a century. Here we resolve these foundational questions by deriving an exact and physically equivalent formulation of the Schrödinger equation as a Real Geometric Flow—a moving-frame evolution on a 2𝑁-dimensional real state space. In this restored framework, the global imaginary unit 𝑖 fully decomposes into a set of local skew-symmetric generators that drive planar rotations in real space, revealing that the traditional complex formalism is a compressed representation of an intrinsic rotational geometry.Within the real geometric flow, energy eigenvalues appear as the Curvatures of the state trajectory, energy gaps correspond to Torsions that couple internal planes—naturally generating the geometry of quantum spin—and quantum phase emerges naturally as the Holonomy of the real moving frame. This formulation preserves the full empirical content of quantum mechanics while exposing the geometric mechanisms hidden beneath its notation, providing the first coherent explanation of curvature, torsion, non-commutativity, spin behavior, and quantum phase within a single framework.By demonstrating that the algebraic postulates of quantum mechanics arise from a deeper geometric order—one that stands alongside curvature-based theories such as General Relativity—this work establishes a unified differential-geometric foundation for quantum dynamics.It opens new directions for quantum control, quantum information, and fundamental physics.
We develop a real-variable mechanics in which complex quantum dynamics is not postulated at the microscopic starting point. The central observation is that integration by parts does more than generate formal boundary terms: in a medium with defects, interfaces, punctures, grains, or excised sets, those boundary terms encode the admissible transport law. Dirichlet, Neumann, and Robin boundary conditions therefore become dynamical selectors for absorption, reflection, and partial reflection-reaction. Robin structure is especially important because the same boundary parameter controls boundary local time in diffusion and a momentum-dependent reflection phase in wave mechanics. We combine this with an Eulerian--Lagrangian description of transport, a symmetric/antisymmetric tensor decomposition, and a compatible antisymmetric two-form. On an oriented two-plane the normalized antisymmetric transport operator satisfies J^2=-I, furnishing a real complex structure without inserting the scalar 'i' by hand. Nelson-type forward/backward stochastic kinematics then produces the continuity equation, quantum potential, and Schrodinger form, while closed defect loops yield Berry-like holonomy. A Glauber master-equation route supplies a discrete stochastic precursor. Bell correlations are treated as an endpoint test of globally prepared nonseparable transport: Bell's theorem is retained in full, so the construction is not a Bell-local hidden-variable model. Rather, it proposes that local propagation can coexist with a globally prepared holonomy/correlation state whose measurement statistics need not factorize. Finally, we connect the symmetric transport sector to emergent 3-geometry, entanglement-area structure, and loop-quantum-gravity-style geometric observables. The paper separates established mathematics from the proposed synthesis and lists numerical and experimental falsification tests.
Abstract We introduce a phase-geometric framework in which time evolution is governed by a covariant derivative defined over a multi-carrier phase space. The associated connection induces a non-abelian curvature whose holonomy generates measurable phase-transport effects. Within this unified geometric setting, the quantum–classical transition, phase-channel mixing, and time-transport anomalies arise from a single underlying mechanism. In contrast to conventional approaches, where gauge structures are imposed externally, the connection emerges intrinsically from the phase geometry itself. The framework yields calculable thresholds for classicalization and leads to novel, testable predictions based on curvature-induced phase holonomy.
We develop a unified framework in which quantum mechanics is assumed to emerge from combinatorial configuration spaces under evolution, curvature, and symmetry constraints. Starting from general discrete configurations such as permutations, tilings, and causal sets, we show that entropy and statistical ensembles arise naturally from counting arguments. Dynamical evolution leads to diffusion and irreversible behavior, while the presence of defects and holonomy introduces geometric phase structure. We demonstrate that invariance under compact symmetry groups, enforced via Haar measure, necessitates a transition from probabilities to amplitudes, yielding unitary and time-reversal symmetric dynamics. This provides a possible derivation of quantum mechanics from combinatorial and geometric principles, with applications to transport theory, nonequilibrium systems, and emergent spacetime.
Non-Hermitian systems exhibit spectral and topological phenomena absent in Hermitian physics; however, their geometric characterization remains subtle due to the intrinsic ambiguity of biorthogonal eigenspaces. Since left and right eigenvectors are not related by Hermitian conjugation, the associated Berry connection is generally nonunique, leading to complex geometric phases and ambiguously defined holonomies. Here we formulate a covariant geometric framework for non-Hermitian quantum systems based on the metric structure of the underlying Hilbert space. We show that, in the quantum regime with continuous state evolution, the conventional Berry connection and the associated Berry holonomy over closed parameter-space loops can be consistently defined only in the pseudo-Hermitian limit, where the spectrum is real. For generic non-Hermitian Hamiltonians with complex spectra, the relevant geometric object is instead the Aharonov--Anandan holonomy associated with cyclic evolution in projective Hilbert space. Within the pseudo-Hermitian regime, we construct a unique Hermitian Berry connection that is covariant under arbitrary GL(N,C){\rm GL}(N,\mathbb C)GL(N,C) frame transformations and reduces to the standard Berry connection in the Hermitian limit. The resulting formalism separates the intrinsic geometry of the Hamiltonian eigenspace from contributions arising from the parameter dependence of the Hilbert-space metric, revealing that the conventional biorthogonal formulation generally mixes these distinct geometric effects. Consequently, geometric phases, synthetic gauge fields, and topological characteristics commonly attributed to non-Hermitian eigenspace geometry may, in part, originate from the underlying metric structure. Our framework therefore provides a consistent geometric foundation for Berry phases, non-Abelian holonomies, and topological invariants in non-Hermitian quantum systems.
We propose a unified framework in which quantum dynamics, gauge interactions, and gravitational behavior arise from a common operator-based microscopic structure. The approach is based on a complex operator composed of two Hermitian components whose non-commutativity generates interaction effects. A positive density operator is constructed, and entropy is used as a central organizing principle connecting microscopic and macroscopic physics. Under general assumptions, the formalism reproduces unitary quantum evolution, provides a mechanism for the emergence of gauge structure, and connects entropy variation to gravitational dynamics. The framework is illustrated through an explicit solvable model demonstrating how interaction strength influences thermodynamic behavior. This work establishes a concrete mathematical basis for exploring a unified origin of fundamental interactions.