We report the discovery of a new class of critical phenomena in open quantum systems that is not governed by divergence of correlation length. In contrast to the standard paradigm, where criticality is identified by ξ → ∞, we demonstrate the existence of regimes characterized by: Δ → 0, Γ > 0, ξ = O(1), where Δ is the partition gap and Γ is the switching rate of optimal decompositions. We show that such systems exhibit a universal modular scaling law: ν(λ) ∼ 1 log λ, derived from the spectral structure of the modular generator K = −log ρ. This scaling defines a new diagnostic observable independent of spatial correlations. We formulate a hard, experimentally testable prediction: Ξ(λ) = ν(λ) · log λ → 1, which provides a falsifiable signature of modular criticality accessible in quantum simulators. The results establish a new notion of criticality rooted in spectral redistribution, commutator dynamics, and information geometry, rather than correlation length. This reveals a previously unrecognized universality class applicable to open quantum systems, non-equilibrium dynamics, and information-theoretic regimes.
We report the discovery of a new class of critical phenomena in open quantum systems that is not governed by divergence of correlation length. In contrast to the standard paradigm, where criticality is identified by ξ → ∞, we demonstrate the existence of regimes characterized by: Δ → 0, Γ > 0, ξ = O(1), where Δ is the partition gap and Γ is the switching rate of optimal decompositions. We show that such systems exhibit a universal modular scaling law: ν(λ) ∼ 1 log λ, derived from the spectral structure of the modular generator K = −log ρ. This scaling defines a new diagnostic observable independent of spatial correlations. We formulate a hard, experimentally testable prediction: Ξ(λ) = ν(λ) · log λ → 1, which provides a falsifiable signature of modular criticality accessible in quantum simulators. The results establish a new notion of criticality rooted in spectral redistribution, commutator dynamics, and information geometry, rather than correlation length. This reveals a previously unrecognized universality class applicable to open quantum systems, non-equilibrium dynamics, and information-theoretic regimes.
We develop a mathematically rigorous and experimentally testable framework for the classification of physical regimes based on the modular structure of quantum states. The central object of the theory is the modular generator K = −log ρ, which provides a unified language for spectral, geometric, and information-theoretic diagnostics. We introduce a universal instrument panel (MSRO: Modular–Spectral RG Observables) that integrates spectral quantiles, commutator-based response functions, partition-based locality diagnostics, and information-geometric structures. A key requirement of the framework is strong portability: the same diagnostic protocol applies across multiple domains—including open quantum systems, information geometry, entanglement-based models, and RG-like flows—without domain-specific retuning. The main result of the work is the derivation of a universal and experimentally testable scaling law for the modular response signal: ν(λ) ∼ 1 log λ, which characterizes critical regimes in a wide class of quantum systems. We prove that this scaling emerges from spectral asymptotics of the modular operator and establish a strict equivalence between spectral, geometric, and information-theoretic descriptions of criticality: ν ↔ k(q) ↔ I(λ) ↔ K ↔ R ↔ Δ. The framework is supported by functional analytic results (including Fr´echet differentiability of log ρ), operator inequalities (Golden–Thompson, monotonicity of relative entropy), and stability estimates. We further provide a concrete experimental protocol for quantum simulators, including statistical error bounds and Fisher information constraints, making the prediction directly testable. Beyond regime classification, the results suggest a new perspective on criticality as a geometric phenomenon associated with vanishing modular curvature. The approach opens pathways toward large-N limits, quantum field extensions, and the discovery of new classes of non-standard critical behavior.
We develop a structural framework in which physical reality is derived from the spectral properties of quantum states. Within the approach of Universal Modular Dynamics (UMD), the density operator ρ is taken as the fundamental object, and its modular generator K =−log ρ provides a representation of informational content. We show that the distribution of modular energies, defined by the spectrum of K, serves as a primary structure from which higher-level physical organization emerges. In particular, we demonstrate how spectral distributions give rise to stable structures, induce locality through optimal partitioning, and generate geometric relations via correlation-based distances. Dynamics is introduced as an intrinsic ordering of states under modular evolution, while renormalization appears as a spectral phenomenon governed by statistical properties of the modular spectrum. This establishes a connection between informational structure and physical scale. The resulting construction defines a sequential chain of emergence, ρ → p(k) → structure → locality → geometry → dynamics → scale, in which each level arises from properties of the previous one without introducing external assumptions. This work provides a unified perspective in which physical structure is understood as an emergent consequence of spectral information encoded in quantum states.
We propose a reconstruction of physical theory based on the principle of distinguishability, formulated within the framework of Universal Modular Dynamics (UMD). Instead of assuming spacetime, fields, or dynamical laws as fundamental, we begin with a minimal relational structure defined by distinguishable proto-states. We show that consistency requirements on distinguishability lead naturally to a probabilistic structure, whose basis-invariant representation is given by the density operator ρ. The associated modular generator K = −log ρ encodes the intrinsic organization of the system, while its spectral distribution provides a complete description of informational structure. Within this framework, dynamics is reinterpreted as a flow in the space of states, and the renormalization group is identified with spectral evolution of ρ. Phase structure emerges from the behavior of optimal partitions, leading to an operational notion of criticality defined by landscape flatness and switching rates. We demonstrate that geometry, gauge structure, and gravitational behavior arise as emergent phenomena associated with specific dynamical regimes. In particular, gauge symmetry is interpreted as access-relative redundancy, and spacetime structure appears as an effective description of underlying spectral organization. The framework is supported by a computational program that introduces operational diagnostics, including spectral observables, modular commutators, and phase classification criteria. These tools allow for numerical exploration and identification of domains of validity. The results suggest that a unified description of physical reality can be constructed from a minimal informational ontology, in which all structures arise from intrinsic properties of the density operator and its modular dynamics.
We present a minimal and testable mechanism for the emergence of spacetime from quantum information within the framework of Universal Modular Dynamics (UMD). Starting from the density operator ρ and the modular generator K = −log ρ, we construct a robust operator-level geometry via commutator structures. We demonstrate that all static information-theoretic constructions—including entropy, mutual information, and spectral embeddings—fail to generate a consistent notion of spacetime. We then introduce dynamical diagnostics based on the propagation of distinguishability and show that spacetime emerges if and only if distinguishability propagates with finite speed and maintains locality, forming a light-cone structure. This leads to a phase classification of quantum dynamics into three regimes: no propagation, fast mixing, and localized propagation, the latter uniquely corresponding to emergent spacetime. Our results establish spacetime as a dynamical phase rather than a fundamental structure and provide a concrete, falsifiable criterion for its existence.
We present a unified theoretical framework, termed TRUE (Théorie Redistributive Universelle Évolutive), to describe the universal regularities observed in quantum critical systems beyond the Fermi liquid paradigm. We introduce a universal invariant \gamma_0 = 0.13648, derived analytically from the Koszul-Fisher curvature constraint on the symplectic manifold of critical phases, without recourse to any empirical fitting. The effective spectral dimension \tau of the dissipation phase space is defined as the invariant trace of the spectral dissipation tensor. We show that the 0\text{D} \to 1\text{D} crossover (unitary Kondo regime) leads to \tau = \sqrt{2}, whose combination with the curvature constraint yields the characteristic equation x^2 - x + \frac{\sqrt{2}}{12} = 0, whose roots are exactly \gamma_0 = 0.13648 and 1 - \gamma_0 = 0.86352. Quantitative validation is performed on five independent classes of materials (strange metals, iron pnictides, magic-angle graphene, Bechgaard salts, InAs nanowires), with deviations below 5% from the predicted invariant. We discuss the validity conditions of the framework, notably the spatial coherence extension condition \xi > 0, and propose a covariant tensor formalism anchored in Koszul-Souriau information geometry.
We propose a strong notion of portability for a unified “instrument panel” intended to operate across four domains: open quantum systems (OQS), information geometry (IG), entanglement-based emergent geometry/gravity (EG), and renormalization group (RG) flow. The panel is defined solely from a density operator ρ and its modular generator K = −log ρ (and, when needed, a visible reduction ρvis). It combines spectral profile coordinates, observable-facing modular commutator diagnostics, operational locality/criticality markers based on optimal correlation factorization, correlation-graph geometry with stability certification, and optional backreaction links. Strong portability is formulated as a transport contract: the same panel, the same gates, and the same validation protocol are applied across domains with only minimal domain adapters that declare the flow coordinate and the visible subsystem. We provide an explicit portability scorecard, robustness checks, and a strict failure-domain taxonomy to prevent overclaim.