In this work, we present a novel unified equation of state (UEOS) that integrates thermodynamic variables across all phases of matter, challenging longstanding paradigms in quantum mechanics and statistical physics. By deriving the UEOS from first principles combining relativistic invariance and nonlocal field interactions, we demonstrate that particle-wave duality emerges as an artifact of incomplete classical approximations rather than a fundamental property of quantum systems. Our analysis reveals those apparent dual behaviors in phenomena such as the double-slit experiment stem from emergent statistical fluctuations in the UEOS, effectively debunking the need for intrinsic duality and reconciling quantum observations with a purely field-theoretic framework. Furthermore, entropy is reinterpreted not as a measure of disorder but as a pseudo-thermodynamic quantity arising from incomplete knowledge of the UEOS parameters, resolving paradoxes in information theory and black hole thermodynamics. Finally, the UEOS elucidates the mystery of phase transitions by providing a continuous analytic function that predicts critical points without invoking symmetry breaking or renormalization group flows, offering exact solutions for van der Waals-like behaviors in real gases and superconductors. This unified approach not only simplifies the theoretical landscape but also suggests experimental tests via high-precision calorimetry and interferometry, paving the way for a paradigm shift in foundational physics.
In this work, we present a novel unified equation of state (UEOS) that integrates thermodynamic variables across all phases of matter, challenging longstanding paradigms in quantum mechanics and statistical physics. By deriving the UEOS from first principles combining relativistic invariance and nonlocal field interactions, we demonstrate that particle-wave duality emerges as an artifact of incomplete classical approximations rather than a fundamental property of quantum systems. Our analysis reveals those apparent dual behaviors in phenomena such as the double-slit experiment stem from emergent statistical fluctuations in the UEOS, effectively debunking the need for intrinsic duality and reconciling quantum observations with a purely field-theoretic framework. Furthermore, entropy is reinterpreted not as a measure of disorder but as a pseudo-thermodynamic quantity arising from incomplete knowledge of the UEOS parameters, resolving paradoxes in information theory and black hole thermodynamics. Finally, the UEOS elucidates the mystery of phase transitions by providing a continuous analytic function that predicts critical points without invoking symmetry breaking or renormalization group flows, offering exact solutions for van der Waals-like behaviors in real gases and superconductors. This unified approach not only simplifies the theoretical landscape but also suggests experimental tests via high-precision calorimetry and interferometry, paving the way for a paradigm shift in foundational physics.
Abstract: This study proposes a unified framework that integrates topological quantum field theories with statistical mechanics to provide a comprehensive understanding of quantum states and dynamics. The problem of reconciling the quantum mechanical description of microscopic systems with macroscopic statistical behavior is addressed by exploring the relationship between topological invariants and thermodynamic properties in quantum systems. The methodology involves the development of a mathematical model that combines the abstract principles of topological quantum field theory with the probabilistic approaches of statistical mechanics, utilizing tensor calculus and advanced mathematical physics tools. Key results indicate that the proposed framework offers new insights into quantum phase transitions, critical phenomena, and the thermodynamic behavior of quantum systems, especially in systems exhibiting topological phases. The framework is further evaluated through a series of theoretical simulations, demonstrating its applicability to quantum information science, condensed matter physics, and quantum technology applications. The implications of this research are significant, providing a foundation for the development of new quantum technologies, such as quantum computing and quantum materials, and contributing to a deeper understanding of the connections between topological properties and statistical mechanics in quantum systems. Keywords: Topological Quantum Field Theory, Statistical Mechanics, Quantum States, Quantum Dynamics, Phase Transitions, Critical Phenomena, Quantum Computing, Quantum Materials, Thermodynamics, Topological Phases, Quantum Information Science.
This work presents an extended, mathematically complete formulation of the Information Geometry Unification Principle (IGUP), a foundational framework in which quantum mechanics, statistical thermodynamics, general relativity, and spacetime geometry emerge from a single information-theoretic ontology. We begin with rigorous axioms defining information as the primary physical substance, then systematically construct the Bures–Fisher–Rao metric on the manifold of quantum density matrices. We derive the universal information action functional and perform full variational derivations to obtain the unified field equations. We show explicitly how standard physical theories including the Schrödinger equation, Heisenberg picture, Liouville mechanics, classical thermodynamics, and Einstein field equations are recovered in appropriate limiting regimes. We further derive geometric expressions for entanglement, entropy, temperature, energy, and force. The theory resolves longstanding conceptual tensions between unitary quantum evolution and gravitational irreversibility, provides a natural resolution to the black hole information paradox, and yields eight concrete, experimentally testable predictions. This extended version includes full tensor calculus, covariant derivatives, curvature expansions, and limit theorems, amounting to a self-contained theory of everything based on Geometry=Information.
This work presents a unified, realistic, and mechanically grounded interpretation of fundamental physics across all scales, from quarks and elementary particles to atoms, macroscopic bodies, planetary motion, and black holes. The proposed framework provides a single coherent physical description capable of reproducing and explaining, within a common dynamical structure, the full range of phenomena traditionally treated separately by general relativity, quantum mechanics, and quantum electrodynamics. Within this approach, long-standing conceptual problems such as wave–particle duality, quantum interference, entanglement, and wavefunction collapse are not postulated as fundamental features of nature, but emerge naturally as dynamical properties of a physically real medium. The apparent dual behavior of matter and radiation, as well as nonlocal quantum correlations, arise from coherent and topologically constrained excitations of this medium, without invoking probabilistic ontologies or nonphysical abstractions. The theory is based on a revised physical concept of space, treated as a real superfluid medium endowed with density, elasticity, viscosity, permittivity, permeability, and a very small but non-zero electrical conductivity. In this model, space is no longer a passive geometric background, but an active physical system capable of storing, transmitting, and dissipating energy.Mass is interpreted as an isotropic compression of the superfluid, electric charge as an oriented torsional configuration, and fields as elastic stress and vorticity distributions of the medium itself. Electromagnetic and gravitational waves are described as propagating perturbations of the superfluid, while particles correspond to stable solitonic configurations sustained by the medium dynamics.At the microscopic level, starting from classical fluid equations (continuity and Euler equations) and applying the Madelung transformation, the Schrödinger equation is shown to emerge as a compact complex representation of the underlying real fluid dynamics, rather than as a fundamental postulate. Quantum phenomena such as quantization, tunneling, spin, and exclusion principles follow from stability, coherence, and topological constraints of solitonic wave structures. On cosmological scales, the same framework provides a unified interpretation of redshift, large-scale expansion phenomena, and the cosmic microwave background as cumulative dynamical and dissipative effects of wave propagation within the superfluid medium, rather than as consequences of metric expansion alone. Effects commonly attributed to dark matter and dark energy are reinterpreted as emergent manifestations of spatial density gradients, elastic stresses, and dissipative properties of the superfluid, without introducing additional unknown components. A wide range of experimentally verified phenomena—including the photoelectric effect, Compton scattering, Zeeman–Stark effects, the Aharonov–Bohm effect, Casimir effect, Unruh radiation, and cosmological attenuation effects—are consistently described within this unified framework. The proposed model offers an alternative foundational paradigm for physics, in which space, matter, and interactions emerge from a single physically intelligible dynamical system, restoring a continuous and causal description of nature from microscopic to cosmological scales.
IFT-ISE is a unified quantum–informational framework in which wave–particle behavior emerges from the interaction between informational structure, geometry, and time. The model extends the standard photonic Hilbert space by introducing an internal informational subsystem, not as a new force or interaction, but as a generator of relational constraints. The framework combines Informational Field Theory (IFT)—where spatial probability distributions arise from local informational entropy gradients—with Internal State Encoding (ISE), a discrete informational basis governing the accessibility of particle-like states. Within this perspective, informational asymmetry does not induce collapse through measurement, but generates relational time and state distinguishability within the local informational geometry. Since photons possess no proper time, the emergence of even minimal relational time renders wave-like propagation incompatible, enforcing particle-like behavior without invoking observer-induced collapse. This reinterpretation provides a physically transparent explanation for the extreme sensitivity of the double-slit experiment to infinitesimal which-path information. IFT-ISE reconstructs the double-slit experiment, predicts upstream coherence modulation prior to slit interaction, and extends naturally to black-hole horizons, where extreme informational geometry suppresses temporal accessibility and amplifies informational structure. Mathematical derivations, conceptual diagrams, and experimentally testable predictions are provided, offering a coherent informational foundation for quantum optical and gravitational boundary phenomena.
This paper presents the definitive thermodynamic formulation of the recently established unified quantum phase space framework. By operating within a strictly positive joint distribution that unifies coordinate and momentum representations without operator expansions, we introduce a novel formulation of quantum entropy based on the classical Shannon-Boltzmann approach. We demonstrate that for any pure or mixed state, the total phase-space entropy decouples into the linear sum of structural spatial and momentum entropies. Utilizing the recently derived equation of motion for hybrid flow, we expose a purely internal, structural mechanism for quantum irreversibility and the arrow of time, arising directly from Fourier duality and phase-space lattice dynamics rather than external environmental coupling. The dynamic behavior of entropy production is analyzed. We provide compact, rigorous quantitative validations by demonstrating how free wave-packet dispersion represents natural decoherence and how the maximization of hybrid entropy naturally yields the classical-quantum Boltzmann-Gibbs distribution. These results establish a stable bridge between quantum mechanics, information theory, and macroscopic thermodynamics.
Why does matter possess wave-like properties? Is wave-particle duality an inherent dual nature of matter, or merely a projection of a deeper underlying physical structure under two distinct observational perspectives? This paper presents a rigorous first-principles derivation of matter wave dynamics within the axiomatic framework of Time Field Theory (TFT). The entire derivation relies solely on two core axioms: local intrinsic total velocity conservation and metric self-consistency (flux conservation), without introducing any extra postulates. Following the logical sequence of ontological foundation, phase derivation, wave generation, hierarchical classification, physical correspondence, extreme-case verification, and unified spectrum construction, this paper first establishes the core ontological premise that matter corresponds to localized condensed states of the time field. It then derives the geometric structure of the existence phase angle on the unit circle of the complex plane from the velocity conservation axiom, revealing the fundamental origin of intrinsic material phases. On this basis, the de Broglie relations are strictly derived, eliminating the dualistic contradiction between particle and wave characteristics. This work further distinguishes two distinct wave regimes: intrinsic waves originating from phase evolution within condensed states, and apparent waves arising from the global spatial translation of field distributions, which are respectively mapped onto electromagnetic waves and gravitational waves as two classes of physical reality. Using black hole horizons as an extreme physical testbed, we demonstrate that intrinsic wave phenomena vanish completely at time-freezing surfaces while apparent wave behaviors remain intact, providing a unified explanation for the observational fact that black holes emit no light yet produce gravitational waves. We also clarify the ontological origin of black hole darkness: light is not trapped by gravity, but the physical conditions required for photon generation cease to hold at time-freezing surfaces. Finally, we construct a continuous spectrum of wave behaviors ranging from the vacuum ground state to black hole horizons. This paper proves that wave-like behavior is not a binary ”present/absent” attribute of matter, but a continuous function of the condensation strength of the time field. Quantum mechanics and classical mechanics do not describe two separate physical worlds; instead, they represent two limiting regimes of a single universal time field under different condensation levels.