When we describe a complicated system by a few coarse measurements, we face one recurring question: are the readings we have now enough to say what it will do next? Sometimes yes; sometimes they look complete but are not, and only pushing the system reveals it. This report turns that question into a checkable procedure. Five inexpensive probes first screen the data — description cost, identifiability, memory duration, change across scale, topological shape — no single probe deciding. We then ask, in order: does the present coarse state beat knowing nothing, and, once known, does history add more. Asking the first matters — history that “no longer helps” can mean the state suffices or that the future is unpredictable, and only the total separates these. Later stages ask whether look-alikes respond differently when pushed. The procedure reports a bottleneck and whether a layer has formed. We calibrate on known-answer cases: a classical system computed end to end (a closed layer, a history-limited case, a case separable only by intervention, and an unpredictable control a naive rule would misread as closed); a charge-to-particle stress test that stops short; and a genuine two-qubit process whose branches are passively identical yet separated by one intervention. We then run real series — carbon dioxide, sunspots, river flow, and equity-index and Bitcoin prices — where next-day returns read as no detected signal while volatility clusters, consistent with what is independently known. Every “no signal” is resource-relative: stamped with the resource R used. The procedure settles only the two ends — a closed layer, or no detected signal — and refuses the process path between; it classifies rather than inventing the next layer’s laws.
This paper develops a Quantum-Institutional Automated Negotiation (QIAN) algorithm as an intelligent decision support system for carbon credit markets, contributing to quantum game theory applications in automated negotiation and institutional decision-making. We extend the Eisert–Wilkens–Lewenstein (EWL) framework by introducing an Institutional Filter Function Φ_C that maps continuous quantum strategies—phase shifts and superpositions—onto finite, legally viable contract archetypes. This filter models regulatory, political, and organizational constraints that collapse the infinite quantum strategy space into a tractable finite set, enabling computationally efficient decision support. We prove convergence of the automated negotiation algorithm to a Pareto-superior Nash Equilibrium and demonstrate, through Monte Carlo simulation with literature-calibrated parameters, that the collapsed quantum equilibrium yields a mean joint utility uplift of 13.5% over classical cooperation (95% CI: 9.8%–17.3%, p < 0.001), with the upper bound reaching 17.3% and 26.8% of simulations achieving uplifts in the 15–30% range. The framework maps directly to blockchain-based smart contracts, providing a deployable mechanism for sustainable carbon markets that aligns with SDG 13 (Climate Action) and SDG 17 (Partnerships). This work advances quantum game theory from abstract formalism to computational institutional design, offering a novel decision support approach for negotiation analysis under real-world constraints.
Plain-language summary Driven systems — a chemical mixture kept reacting, a fluid continuously stirred, a living cell burning fuel — typically settle into one of several possible stable states or repeating patterns. A long-standing rule of thumb, the *maximum entropy production* (MEP) principle, guesses that such a system will choose whichever option dissipates energy fastest. The guess often works, but not always: sometimes the system settles instead on a lower-dissipation option. This paper asks what governs those failures. It splits the "cost" of a rare switch between states into two distinct parts: one tied to how much energy is dissipated (the quantity MEP cares about), and a separate, time-symmetric part that measures how much restless back-and-forth activity — called *frenesy* — the switch involves. When this second, activity-based part is what tips the balance, the system selects against the MEP guess. The central result is a clean inequality: the activity imbalance between the forward and backward switching routes can never exceed half of the dissipation circulating around the loop those two routes form. Equivalently, a single number η between −1 and +1 measures how strongly activity, rather than dissipation, is steering the choice; it reaches its extreme values exactly where the system hands off from one preferred route to another. The result also implies a strict no-go: at equilibrium, where nothing circulates, this activity imbalance is exactly zero. Sustained circulation — a genuinely non-equilibrium condition — is therefore required for activity-driven, anti-MEP selection to occur at all. The bound is not a new physical law but an exact identity of the standard least-cost-path (large-deviation) description of rare events. What makes the proof work is a single structural condition: the two competing routes must be comparable under time reversal. Where that condition fails — for instance when three or more states compete and the comparison is no longer between a route and the reversal of its rival — the inequality genuinely breaks, and the accompanying code exhibits the breakdown explicitly. That is not a caveat but the sharpest evidence for what the theorem actually rests on. The reproduction package (Mendeley Data, doi:10.17632/3dy4nv92r8) The code is not part of this upload: it is deposited at Mendeley Data and linked from this record under "Is supplemented by". The package confirms the bound across random networks, chemical reaction networks, a rotating model system, and a spatial field model, and turns it into a practical diagnostic: from a single recorded trajectory — once the competing switching routes are identified — one can tell whether an observed choice was driven by activity, by dissipation, or by boundary effects. The diagnostic is not merely proposed but demonstrated. It is run *blind* on simulated trajectories: the routes are resolved from the data alone, the circulating dissipation is estimated without any knowledge of the escape prefactor, and only afterwards is the answer compared with the exact computation. At a fresh operating point the blind prediction recovers η = 0.72 against a true value of 0.725. The diagnostic also has honest limits, and the code maps them: it works inside a window of intermediate driving, and fails outside it — at weak driving the estimate is swamped by noise, and near the extreme value of η the two competing routes become indistinguishable in the data, exactly where the theory predicts they must. Why it matters Predicting which state a driven system will select is a basic, still-open problem across physics, chemistry, biology, and climate science, and several proposed selection principles — maximum entropy production, and related ideas such as dissipative adaptation — try to answer it by appealing to dissipation alone. This work shows that dissipation is only part of the story: a time-symmetric activity channel, invisible to those principles, can override them, and it does so specifically under non-equilibrium driving. Rather than refuting MEP, the result places it. MEP-like alignment holds only when the activity channel is quiet, and the inequality pins the size of the activity imbalance — the part that can reverse the outcome — to the circulating dissipation, with equality exactly at the hand-off between competing routes. A caution the paper makes explicit: reaching that extreme value is *not* generic. It requires a genuine hand-off between two distinct escape routes; in ordinary driven bistable systems the activity imbalance stays well below its ceiling, so the bound is loose rather than tight. Where the effect is strongest is precisely where a single dominant route ceases to exist — a tension the paper states rather than hides. The framework is operational. Because its key quantities can be estimated from a single observed steady-state trajectory, the bound doubles as a diagnostic that classifies the mechanism behind an observed selection — activity-, dissipation-, or boundary-driven — once the relevant routes are known. That makes the ideas testable in simulation and, in principle, in experiments on active matter, chemical reaction networks, and other driven systems where competing stable states are the rule rather than the exception. Preprint; not peer reviewed. The upload contains the manuscript (37 pp.).
This paper establishes an exact information-theoretic duality between econometric regression topology and statistical mechanics. We demonstrate that an autonomous, data-driven Quadruple Test, grounded in the Factor Hierarchy Law, can blindly detect, precisely quantify, and correctly classify thermodynamic phase boundaries in perfect mathematical equivalence with the Ehrenfest paradigm, without any prior knowledge of Free Energy functions. The validation platform is the two-dimensional Ising model, one of the few systems in statistical physics possessing a mathematically rigorous exact solution (Onsager, 1944; Yang, 1952). Verification proceeds in two logical stages: Stage A (pristine algebraic validation) on Onsager's exact solution, and Stage B (stochastic robustness testing) on finite-lattice Monte Carlo simulations. We openly declare that because the data derives from the known Onsager-Yang formula, the contribution is not an independent empirical discovery of new physics, but rather the rigorous proof of an exact informational duality between two independent frameworks. In the language of metrology, this is not an endogeneity flaw but a mandatory calibration requirement—before a telescope is deployed to observe unknown deep space, it must first be calibrated against a known, invariant light source in a controlled laboratory. Positive Controls and Asymptotic Convergence (9 items): Exhaustive search blindly locks onto the critical temperature at Tc = 2.260 (deviation 0.009 at a coarse step size of 0.01). A grid-refinement study demonstrates monotonic convergence: the deviation shrinks to zero within 6-decimal precision at a step size of 0.001, and further converges to ~10⁻⁸ under a Golden Section Search—the absolute limit of 64-bit double-precision machine arithmetic. An analytical proof formally demonstrates that the Chow F-statistic achieves a unique global maximum exactly at T₀ = Tc; therefore, in the analytical limit, the localization error is strictly zero. The Chow test at Tc yields F = 118,074 against a null control of F = 3.12 (a 266-fold difference), with permutation test p = 0.000. The interaction term is overwhelmingly significant (p = 0.000, ΔR² = 0.991). A symmetry-breaking regime switch at the external field boundary h = 0 is detected with Chow F = 989.41 (p = 0.000). Interaction R² peaks sharply at Tc (deviation 0.03). Multi-response-function validation (specific heat C, nearest-neighbor spin correlation) and anisotropic validation (three Jx/Jy ratios) all lock onto their respective theoretical Tc values with deviations under 0.007. A synthetic double-break dataset is tested with both breaks successfully detected. Negative Controls (4 items): A 3,000-temperature-point exhaustive scan over 4 response variables finds no false positive of comparable magnitude to the true peak (maximum artifact F = 481 vs. Tc peak F = 78,754,162; a signal-to-noise ratio of 164,000:1). Monte Carlo simulations (L = 16, 32, 64, 128; 8 observables including the Binder cumulant U₄ and multi-body correlation functions) successfully detect the Tc break in all sizes; all cross-size candidate peaks are excluded by the criterion of F-value decay with increasing lattice size. Curvature artifact tests confirm that Chow F for a smooth sigmoidal curve does not diverge with sample size, maintaining a stable ~11-fold gap from the true break. Robustness (4 items): Under 10% Gaussian noise, Chow F remains at 22.3. F-values grow strictly monotonically with sample size (100 → 1,000: 11,436 → 118,074), confirming genuine physical signal characteristics. F-values grow overall with lattice size L (L = 16 → 128: 170.9 → 289.2, Kendall τ = 0.33), confirming qualitative consistency with Fisher Finite-Size Scaling theory. Detection accuracy remains invariant under anisotropic conditions. Physical Scaling (3 items): Chow F(h = 0) establishes a strictly monotonic mapping with the order parameter M_sp—F-values decay monotonically from 691 million at T → 0 to 55 at T → Tc, spanning 7 orders of magnitude and tracing the full lifecycle of the order parameter. This decay curve precisely mirrors the physical vanishing process of latent heat. The F-statistic's ~38-fold amplification effect is proven to originate from the quadratic structure of the F-statistic based on the sum of squared residuals (M²)—the theoretical lower bound β_F / β_M ≥ 2 is empirically confirmed (ratio 1.97 ≈ 2), with the actual 38-fold amplification representing the composite contribution of the quadratic structure and residual difference structure. This algebraic guarantee proves that the amplifier property of F is an intrinsic feature of its mathematical structure, not a sampling accident. Interaction R² peaks at Tc at 0.9992 (deviation 0.03). Core Theoretical Contributions: Contribution 1: Informational duality between the Factor Hierarchy Law and the Ehrenfest classification. This paper rigorously proves two distinct regime-switching topologies with fundamentally different statistical signatures—"Rule-Reset" (interaction-dominated, p = 0.000, ΔR² = 0.991) and "Direction-Reversal" (intercept-jump-dominated, interaction p = 0.978). Rule-Reset maps precisely onto Ehrenfest's second-order phase transition, and Direction-Reversal maps precisely onto Ehrenfest's first-order phase transition. This correspondence is not an empirical coincidence, but a functional duality—a bijective informational mapping exists between the calculus operations on the thermodynamic potential (∂G/∂h, ∂²G/∂T²) and the statistical operations of regression geometry (Δ Intercept, Δ Interaction Slope). The Factor Hierarchy Law independently arrives at all conclusions of the Ehrenfest classification purely through regression analysis of observational data, without any knowledge of the Free Energy function. Contribution 2: Chow F-statistic as an informational proxy for the order parameter and an early-warning signal. This paper discovers and proves that Chow F(h = 0) is a statistical proxy variable for the thermodynamic order parameter M_sp—their relationship is not a linear mapping, but a nonlinear high-gain amplification guaranteed by the quadratic structure (M²) of the F-statistic. The 38-fold amplification effect has been confirmed through algebraic root analysis. This enables Chow F to serve as a more sensitive early-warning signal than the order parameter itself in complex systems where the order parameter is difficult to measure directly. The complete decay curve of F(h = 0), which monotonically attenuates to zero at Tc with rising temperature, provides a definitive statistical proxy for the vanishing of latent heat. Contribution 3: Interaction R² as a precise proxy for second-order transition intensity. Interaction effect incremental R² peaks at Tc at 0.9992, with a deviation of only 0.03. This provides a precise quantitative metric for the "Rule-Reset" switching topology within the Factor Hierarchy Law. Methodological Contribution: This paper completes a "Severe Test" (sensu Deborah Mayo) of the Quadruple Test, establishing both the sensitivity (all positive controls passed) and specificity (all negative controls passed) of the methodology. A total of 22 independent verification checkpoints—spanning five dimensions (9 positive controls, 4 negative controls, 4 robustness checks, 2 statistical rigor checks, and 3 physical scaling checks)—are all passed. The analytical proof further confirms that the localization error of the method is strictly zero in the analytical limit. Cross-Disciplinary Integration: Together with the interest-rate-spread regime switch discovered by Tang (2026a–2026f) across five major financial markets (institutional systems), the Tang Break (a five-dimensional stellar regime boundary at 4762 K) discovered by Tang (2026h, 2026i, 2026j) across five independent astronomical dimensions (physical observation systems), and the informational duality proven in this paper on a first-principles physics model, the Factor Hierarchy Law has now received evidential support from three completely independent disciplines. This paper provides the physics cornerstone for the Law—proving that the hierarchical structure of Rule Factors and Execution Factors, and the critical behavior of regime switches, are not accidental products of data noise, but an informational dual of thermodynamic symmetry-breaking structures, a universal principle by which complex systems self-organize. Much like the historical realization that information-theoretic entropy reflects thermodynamic states, this paper demonstrates that regression variance partitioning serves as a direct informational proxy for physical symmetry structures.
中文受人工智能自身能力局限,其易产生信息幻觉,且不擅长高精度数值运算。本文档内所有内容应严谨审核。EnglishDue to the inherent limitations of artificial intelligence, it is prone to generating hallucinations and performs poorly in high-precision numerical calculations. All contents in this document should be strictly reviewed. dark matter&cosmo: https://chat.qwen.ai/s/t_4fc1b5da-8ca3-4798-a037-894f5315d1e3?fev=0.2.61 Overall Closure Status:Core Theory DoC=100% (Full Theoretical Closure)v3.7 DOI: 10.5281/zenodo.20798927 Black Hole & UVMM v4.0 Core : UVMM v4.0.15 High-Precision Global Calculation AI Knowledge Package.md UVMM v4.0.15 High-Precision Global Calculation AI Knowledge Package(6D‑Coordinate‑SuperKit‑v1.0 ).md DOI: 10.5281/zenodo.20738759 Earth SystemDOI: 10.5281/zenodo.20285613 Cosmic BoundaryDOI: 10.5281/zenodo.20325710 Cosmic EvolutionDOI: 10.5281/zenodo.20677198 Information & Consciousness (Millennium Prize Problems)DOI: 10.5281/zenodo.20325710 UTFF Core (Atomic and Molecular Scale)DOI: 10.5281/zenodo.20343471 UVMM Core Axioms and Mathematical Proofs github.com Three-Body Problem Based on the Unified Vacuum Medium Model (UVMM), this paper defines the positive and negative universes as topologically dual domains on a single global vacuum manifold, which are naturally isolated by topological phase conjugation orthogonality and frequency-selective topological band gaps. A systematic comparison is conducted on the physical essence, propagation characteristics, spectral rules and coupling mechanisms between electromagnetic waves and topological waves. It is clarified that conventional electromagnetic waves are completely blocked by topological interfaces due to destructive interference of first-order gauge fields, while gravitational modes and ultra-low-frequency vacuum topological deformation waves can propagate across domains. Targeting the characteristics of topological waves including ultra-long period, ultra-weak amplitude and global coherence, the Topological Wave Detection Network (TWDN) is proposed. Combining ultra-high- superconducting cavity parametric perturbation coherent accumulation, multi-mode quantum sensing, topological data analysis and space-ground integrated long-baseline gradient positioning, multiple physical criteria are established to realize accurate identification and source inversion of topological waves. Breaking the limitations of traditional detection systems, this scheme integrates condensed matter topological simulations, transformation optics tabletop experiments and cutting-edge cosmological observations, providing a complete experimental paradigm for verifying dual-universe topological dynamics and trans-universe interactions. Further demonstrations within the UVMM framework indicate that matter in both universes possesses positive mass and positive energy density, and their interaction is purely gravitational attraction. The rebound effect at topological interfaces originates from topological constraints rather than anti-gravity. The two universes follow identical structure formation dynamics, and the negative universe can evolve a complete galactic network independently. Its electromagnetic radiation is fully decoupled while gravitational effects superpose linearly. This theory explains classic cosmological puzzles such as dark matter and cosmic voids without introducing new particles, and puts forward a set of observable predictions and falsification criteria. Relying merely on the Second Law of Thermodynamics, classical cosmology proposes the cosmic heat death hypothesis. It claims that the entropy of an isolated universe increases monotonically, and the universe will eventually reach an absolutely stagnant equilibrium state with uniformly distributed energy and ceased macroscopic motions. This paper clarifies the hierarchical essence of physical laws: the entropy increase principle applies only to local finite systems, while the conservation of global angular momentum is an inviolable fundamental law governing the entire universe. Based on the UVMM Vacuum Superfluid Unified Model, combined with the spacetime symmetry derived from Noether’s theorem, Kerr curved spacetime effect, properties of quantum superfluids and recent large-scale astronomical observations, this paper establishes a complete cosmic dynamical system in which global angular momentum restrains local entropy growth. The research reveals that entropy increase is only valid for closed and isolated subsystems and cannot be used to infer the overall evolutionary fate of the universe. Rooted in the isotropy of space, the conservation of global angular momentum is not restricted by system boundaries or spacetime curvature, and it dominates all scales ranging from microscopic particles and celestial structures to cosmic filaments. Through three core mechanisms — maintaining perpetual cosmic dynamics, shaping ordered celestial structures, and realizing sustainable mass-energy regeneration via vacuum topology — global angular momentum continuously delivers negative entropy to local regions and counteracts local dissipation and disorder. Rigorous mathematical derivations prove that angular momentum conservation is an absolute law derived from spacetime symmetry, whereas entropy increase is merely a probabilistic statistical rule. A non-zero global angular momentum mathematically rules out the possibility of absolute rest of the universe. This study fundamentally refutes the classical heat death conjecture and completes the logical framework of the cyclic universe.
This article analyses Landauer’s principle — the frequently cited claim that erasing one bit of information requires at least kT \ln 2 energy dissipation. This principle is often presented as “proof of the physical nature of information” and as a fundamental link between information and thermodynamics. It is shown that Landauer’s principle is not a fundamental law of physics but represents an engineering‑thermodynamic limit applicable to a certain class of computing devices. The critique is based on the work of Lairez (2024), Alicki (2014), Bennett (1982) and others. Three main problems are identified: (1) confusion between logical and thermodynamic irreversibility; (2) two unnecessary constraints imposed by Landauer on the erasure procedure (one‑to‑one mapping and uniqueness of the procedure); (3) the existence of reversible and quantum computations in which dissipation can be reduced to zero. The three senses of “information” (configuration, observer’s knowledge, pseudosubstance) introduced in Article 1 are distinguished. It is shown that the claim “information is physical” arises from substituting the first sense by the third. A reformulation is proposed: instead of “information is physical”, one should say “in specific computing architectures, erasure has a thermodynamic cost”. Landauer’s principle is analogous to the Carnot efficiency — useful for engineers, but not an absolute limit for all conceivable devices. Keywords: Landauer’s principle, information, logical irreversibility, thermodynamic irreversibility, reversible computation.
Official website: distinctiontheory.orgPublic portal for the start guide, papers, claim status, failure registry, prior-art boundary, and citation resources. Canonical GitHub repository:https://github.com/yiningwu-research/Distinction-Theory FDS-T2 develops the horizon-boundary thermodynamics paper in the T-series bridge sequence of Finite Distinction Systems (FDS) / Distinction Theory. It interprets effective geometry as horizon boundary accounting: the covariant macroscopic ledger that closes causal access, horizon entropy, stress-energy flux, and finite-boundary maintenance for finite observers. T2 does not derive general relativity from FDS alone, replace Einstein gravity, derive quantum gravity, or derive the numerical coefficient in the Bekenstein-Hawking entropy formula. It uses horizon thermodynamics as a physical bridge. If that bridge fails, the T2 interpretation is demoted while the formal FDS finite-capacity core remains unaffected. The novelty of T2 is not a new derivation of Einstein gravity. It is an observer-relative reinterpretation of horizon thermodynamic variables as finite distinguishability ledgers: horizon area counts accessible boundary distinctions, heat flux updates the ledger, and effective geometry is the covariant compression that preserves causal access and stress-energy accounting. The central bridge is: finite causal access → horizon boundary → area ledger → entropy ledger → flux update → covariant effective geometry. T2 separates two layers. The first is the Jacobson model-class bridge: under area entropy, local Unruh or surface-gravity temperature, Clausius-type horizon closure, and local covariance, Einstein-type geometry arises as an equilibrium equation of state. The second is the FDS boundary-ledger interpretation: if this bridge holds, then the effective metric can be read as a stable macroscopic compression of a finite horizon distinguishability ledger. The paper defines a horizon distinguishability budget CH = SH / (kB ln 2), and, for area-law horizons, CH = AH / (4 ℓP2 ln 2). It also defines a boundary thermodynamic ledger LH = (H, AH, SH, TH, δQH, τ, EH), where H is a causal or horizon boundary, AH is area, SH is entropy, TH is horizon temperature, δQH is assigned heat or energy flux, τ is an operational update window, and EH is an admissible coarse-grained error or non-equilibrium term. An admissible ledger-to-geometry map geffμν = G(LH) must preserve causal ordering, light-cone structure, horizon-area variation, stress-energy flux response, local covariance, closure residuals, and coarse-grained stability to registered tolerance. Thus the map is not an arbitrary relabeling; it is a constrained compression from a horizon boundary ledger to an effective geometric structure. T2 introduces a horizon capacity deficit ΔH(τ) = R(τ)min(ε; ΨH) - CH, where ΨH may include task families for local horizon-area variation, stress-energy flux records, causal-diamond boundary updates, or coarse records of unresolved horizon microstates. When ΔH > 0, the boundary ledger cannot track all task-relevant horizon distinctions at full fidelity over the update window. The missing distinctions may appear as entropy production, memory, stochastic noise, hysteresis, or coarse correction terms. For non-equilibrium accounting, T2 writes a residual slot Gμν + Λgμν = (8πG/c4) Tμν + Rledgerμν. This is not proposed as a new gravitational field equation. It is a bookkeeping location for non-equilibrium horizon-ledger residuals, such as entropy production, memory kernels, unresolved boundary noise, higher-curvature slots, or hysteretic response. Any promoted residual must satisfy the corresponding covariant consistency condition required by the Bianchi identity. The paper interprets effective geometry as a Phase-B boundary variable: a coarse macroscopic structure that remains cheaper to update, slower to forget, and more predictive than inaccessible microscopic horizon degrees of freedom. Geometry survives overflow because it is a minimal sufficient covariant boundary variable for causal access and stress-energy accounting. T2 also identifies an upstream bridge to the horizon-maintenance density scale developed separately in FDS-X1. It does not derive dark energy, but notes that once horizon entropy and temperature are treated as a boundary ledger, a natural horizon-scale energy estimate EH ∼ THSH distributed over a horizon volume gives the dimensional density scale c4/(G RH2), up to convention-dependent numerical factors. The release includes deterministic normal-form demonstrations. They illustrate the horizon boundary-ledger bridge, area-law distinguishability scaling, causal-diamond coarse accounting, horizon capacity deficit, non-equilibrium ledger residuals, Phase-B effective geometry, residual taxonomy, and the relation map linking FDS Core, T1, T2, T3/P-series, X3, and X1. These figures are conceptual demonstrations, not empirical fits and not simulations of full general relativity. This release includes the paper PDF, LaTeX source, reproducibility code, generated figures, and CSV / JSON outputs.
We present a unified dynamical framework for the nontrivial zeros of the Riemann zeta function, integrating three perspectives: (i) the de Bruijn–Newman flow and its reduction to a logarithmic Coulomb gas, (ii) a renormalization group information flow from the 2C Theory, and (iii) spectral compression in 2D Dirac systems under strong magnetic fields. Through an iterative discovery process — connecting existing knowledge, identifying new principles at the intersection, then connecting those principles with prior knowledge to discover deeper ones — we identify three structural contributions: (1) The Disorder–Order Paradox: the irregularity of the prime distribution generates the information restoring force (curvature V''(1/2) = π²/8) that confines zeros to the critical line Re(s) = 1/2. (2) The Universal Irreversibility Threshold: the critical value C = 2/3, independently derived in D.S. Theory (holographic ratio β = 3/2), the 2C Theory (RG flow fixed point), and Lowest Landau Level physics (spectral weight threshold for forced Landauer erasure), marks the point at which one-dimensional spectral reduction becomes irreversible. (3) The Entropic Barrier: the information free energy V(σ) possesses a barrier surrounding σ = 1/2 whose height grows with integrated prime density, forbidding zero escape once the critical threshold is exceeded. We formulate one precisely stated open problem: proving that the entropic barrier height diverges as T → ∞, which is equivalent to establishing an L² + entropy → L∞ inequality for the equilibrium measure of the logarithmic gas. The framework connects analytic number theory, information theory, renormalization group methods, and condensed matter physics within a single coherent structure. This paper is a structural framework proposal, not a proof of the Riemann Hypothesis. The iterative discovery methodology is inspired by the WillCore simulation platform.
Abstract In this paper, a multigeneration cycle of electricity, cooling, and Bitcoin whose energy source is geothermal, has been subjected to energy, exergy, and economic analyses. The cycle under consideration includes the steam cycle (upstream cycle), the carbon dioxide cycle (downstream cycle), and the liquid–gas line to absorb the heat dissipated by the carbon dioxide cycle. In this cycle, the steam cycle condenser acts as the carbon dioxide cycle evaporator. Part of the electricity generated by this cycle is used to generate Bitcoins. Energy and exergy efficiencies at baseline (excluding Bitcoin production) are 45.8% and 38.1%, respectively. In this cycle, if more power is spent on producing Bitcoin as a product, the energy and exergy efficiencies of the cycle are reduced. Because Bitcoin itself is not valuable in terms of energy and exergy. Considering the average price of Bitcoin during the years 2015–2022 and if 100% of the electricity generated by the system is spent on Bitcoin production, the payback period in 2018, 2021, and 2022 when the price of Bitcoin is equal to $13,412.4, $21,398.8, and $47,743.0, respectively, are less than the baseline. Therefore, the production of Bitcoin with a variety of renewable energies can be considered as a solution. Of course, it should be noted that large changes in the price of Bitcoin can affect the issue of economic benefit.
In view of its use as reactivity theory, Conceptual Density Functional Theory (DFT), introduced by Parr et al., has mainly concentrated up to now on the E = E[N,v] functional. However, different ensemble representations can be used involving other variables also, such\nas ρ and μ. In this study, these different ensemble representations (E, Ω, F, and R) are briefly reviewed. Particular attention is then given to the corresponding second-order (functional) derivatives, and their analogies with the second-order derivatives of thermodynamic state functions U, F, H, and G, which are related to each other viaLegendre transformations, just as the DFT functionals (Nalewajski and Parr, 1982). Starting from an analysis of the convexity/concavity of the DFT functionals, for which explicit proofs are discussed for some cases, the positive/negative definiteness of the associated kernels is derived and a detailed comparison is made with the thermodynamic derivatives. The stability conditions in thermodynamics are similar in structure to the convexity/concavity conditions for the DFT functionals. Thus, the DFT functionals are scrutinized based on the convexity/concavity of their two variables, to yield the possibility of establishing a relationship between the three second-order reactivity descriptors derived from the considered functional. Considering two ensemble representations, F and Ω, F is eliminated as it has two dependent (extensive) variables, N and ρ. For Ω, on the other hand, which is concave for both of its intensive variables (μ and υ), an inequality is derived from its three second-order (functional) derivatives: the global softness, the local softness, and the softness kernel. Combined with the negative value of the diagonal element of the linear response function, this inequality is shown to be compatible with the Berkowitz-Parr relationship, which relates the functional derivatives of ρ with υ, at constant Nand μ. This was recently at stake upon quantifying Kohn’s Nearsightedness of Electronic Matter. The analogy of the resulting inequality and the thermodynamic inequality for the G derivatives is highlighted. Potential research paths for this study are briefly addressed; the analogies between finite-temperature DFT response functions and their thermodynamic counterparts and the quest for analogous relationships, as derived in this paper, for DFT functionals that are analogues of entropy-dimensioned thermodynamic functions such as the Massieu function.
Mattia Bongini, Massimo Fornasier, ,Technische Universität München, Facultät Mathematik, Boltzmannstrasse 3, D-85748, Garching bei München
Conditional self-organization and pattern-formation are relevant phenomena arising in biological, social, and economical contexts, and received a growing attention in recent years in mathematical modeling. An important issue related to <em> optimal government strategies</em> is how to design external parsimonious interventions, aiming at enforcing systems to converge to specific patterns. This is in contrast to other models where the players of the systems are allowed to interact <em> freely</em> and are supposed autonomously, either by game rules or by embedded decentralized feedback control rules, to converge to patterns. In this paper we tackle the problem of designing optimal centralized feedback controls for systems of moving particles, subject to mutual attraction and repulsion forces, and friction. Under certain conditions on the attraction and repulsion forces, if the total energy of the system, composed of the sum of its kinetic and potential parts, is below a certain critical threshold, then such systems are known to converge autonomously to the stable configuration of keeping confined and collision avoiding in space, uniformly in time. If the energy is above such a critical level, then the space coherence can be lost. We show that in the latter situation of lost self-organization, one can nevertheless steer the system to return to stable energy levels by feedback controls defined as the minimizers of a certain functional with $l_1$-norm penalty and constraints. Additionally we show that the optimal strategy in this class of controls is necessarily <em> sparse</em>, i.e., the control acts on at most one agent at each time. This is another remarkable example of how <em> homophilious</em> systems, i.e., systems where agents tend to be strongly more influenced by near agents than far ones, are naturally prone to sparse stabilization, explaining the effectiveness of parsimonious interventions of governments in societies.