Generative diffusion models have emerged as a powerful class of models in machine learning, yet a unified theoretical understanding of their operation is still developing. This paper provides an integrated perspective on generative diffusion by connecting the information-theoretic, dynamical, and thermodynamic aspects. We demonstrate that the rate of conditional entropy production during generation (i.e., the generative bandwidth) is directly governed by the expected divergence of the score function’s vector field. This divergence, in turn, is linked to the branching of trajectories and generative bifurcations, which we characterize as symmetry-breaking phase transitions in the energy landscape. Beyond ensemble averages, we demonstrate that symmetry-breaking decisions are revealed by peaks in the variance of pathwise conditional entropy, capturing heterogeneity in how individual trajectories resolve uncertainty. Together, these results establish generative diffusion as a process of controlled, noise-induced symmetry breaking, in which the score function acts as a dynamic nonlinear filter that regulates both the rate and variability of information flow from noise to data.
We develop a geometric foundation of microcanonical thermodynamics in which entropy and its derivatives are determined from the geometry of phase space, rather than being introduced through an a priori ensemble postulate. Once the minimal structure needed to measure constant -- energy manifolds is made explicit, the microcanonical measure emerges as the natural hypersurface measure on each energy shell. Thermodynamics becomes the study of how these shells deform with energy: the entropy is the logarithm of a geometric area, and its derivatives satisfy a deterministic hierarchy of entropy flow equations driven by microcanonical averages of curvature invariants (built from the shape/Weingarten operator and related geometric data). Within this framework, phase transitions correspond to qualitative reorganizations of the geometry of energy manifolds, leaving systematic signatures in the derivatives of the entropy. Two general structural consequences follow. First, we reveal a thermodynamic covariance: the reconstructed thermodynamics is invariant under arbitrary descriptive choices such as reparametrizations and equivalent representations of the same conserved dynamics. Second, a geometric microcanonical equivalence is found: microscopic realizations that share the same geometric content of their energy manifolds (in the sense of entering the curvature sources of the flow) necessarily yield the same microcanonical thermodynamics. We demonstrate the full practical power of the formalism by reconstructing microcanonical response and identifying criticality across paradigmatic systems, from exactly solvable mean-field models to genuinely nontrivial short-range lattice field theories and the 1D long-range XY model with $1/r^α$ interactions.
Eric E. Houghton, Litha Yapi, Nils Haneklaus
et al.
Emerging xenobiotics, such as tetracycline (TC), pose significant risks to both the environment and human health. Adsorption is a recognized method for removing these contaminants, and in this study, fly ash (FA), a by-product of coal combustion, was modified to develop adsorbents. Acid-modified FA (AM-FA) and base-modified FA (BM-FA) were prepared, and zeolite Na-P1 (ZNa-P1) was synthesized via hydrothermal treatment. Adsorption tests revealed that BM-FA and ZNa-P1 removed 76% and 90% of TC, respectively, compared to 35% with unmodified FA. AM-FA had the lowest performance, removing just 11% of TC. ZNa-P1’s superior performance was linked to its high zeolite purity, with a cation exchange capacity (CEC) of 6.37 meq/g and a surface area of 35.7 m<sup>2</sup>/g. Though BM-FA had a larger surface area of 110.8 m<sup>2</sup>/g, it exhibited a lower CEC of 3.42 meq/g. Adsorption efficiency was more closely related to CEC than surface area. Optimal TC removal with ZNa-P1 was achieved at a 7.5 g/L dosage and pH 5. The process followed pseudo second order kinetics and the Langmuir isotherm, with a maximum capacity of 46.34 mg/g at 30 °C. The adsorption thermodynamics indicated that the adsorption was endothermic and spontaneous. The adsorption mechanism of tetracycline on ZNa-P1 involved electrostatic attraction, hydrogen, and ion exchange. This study aligns with SDGs 6 (Clean Water and Sanitation) and 12 (Responsible Consumption and Production).
Dimitrios Mathioulakis, Nikolaos Vasilikos, Panagiotis Kapiris
et al.
The aerodynamic loading of four as well as of six tilted flat plates-panels arranged in tandem and in close proximity to the ground is examined through force and pressure measurements. In the four-plate set up, conducted in an open-circuit wind tunnel, a movable floor is used to vary the ground clearance, and a one-component force balance is employed to measure the drag coefficient Cd of each plate for tilt angles 10° to 90° and for two head-on wind directions, 0° and 180°. An increase in the ground clearance from 20% to 60% of the plates’ chord length, results in a Cd increase of over 40% in the downstream plates, and up to 20% in the leading one. For tilt angles below 40°, the drag on the first plate is up to 25% higher under the 180° wind direction compared to the opposite direction. Pressure distributions are also presented on a series of six much larger plates, examined in a closed-circuit wind tunnel at tilt angles ±30°. While the windward surfaces exhibit relatively uniform pressure distributions, regions of low pressure develop on their suction side, near the plates’ tips leading edge, tending to become uniform streamwise.
Thermodynamics, Descriptive and experimental mechanics
Jordi Farjas, José Antonio González, Daniel Sánchez-Rodríguez
et al.
Local overheating during curing of thermosetting resins is likely to occur for thick laminates or during fast curing. Overheating may lead to heterogeneous mechanical properties along the laminate thickness or even to an uncontrolled reaction. To avoid overheating, most thermoset resin manufacturers recommend a “safe” cure cycle. However, these cure cycles can be improved to shorten cure times in thin laminates and may not be good enough to avoid overheating in thick laminates. In this paper, we propose a new analytical model to determine the critical thickness above which thermal runaway occurs when the laminate is heated at a constant rate up to a constant temperature. The model considers different thermal boundaries between the mould and the laminate, i.e., from a perfect thermal contact to a contact of infinite resistance. The analytical model was corroborated through the numerical integration of the equations governing it and experimental data from the curing process of a thick laminate composed of the commercial VTC401 epoxy resin and M55J carbon fiber system. Model predictions indicate that, under the manufacturer's recommended cure cycle, which includes an initial heating rate of 2 K/min, thermal runaway occurs in laminates thicker than 12.4 mm, aligning with experimental observations. A 20-mm-thick laminate, exceeding this threshold, was cured using a reduced heating rate of 0.3 K/min based on our criteria, successfully preventing overheating. The maximum temperature gradient recorded experimentally remained below 1 °C, confirming the model's prediction of uniform thermalization.
Devasmito Das, Ina Taralova, Jean Jacques Loiseau
et al.
Fractional-order models provide a powerful framework for capturing memory-dependent and viscoelastic dynamics in mechanical systems, which are often inadequately represented by classical integer-order characterizations. This study addresses the identification of dynamic parameters in both single-degree-of-freedom (1-DOF) and three-degree-of-freedom (3-DOF) Duffing oscillators with fractional damping, modeled using the Grünwald–Letnikov characterization. The 1-DOF system includes a cubic nonlinear restoring force and is excited by a harmonic input to induce steady-state oscillations. For both systems, time domain simulations are conducted to capture long-term responses, followed by Fourier decomposition to extract steady-state displacement, velocity, and acceleration signals. These components are combined with a GL-based fractional derivative approximation to construct structured regressor matrices. System parameters—including mass, stiffness, damping, and fractional-order effects—are then estimated using pseudoinverse techniques. The identified models are validated through a comparison of reconstructed and original trajectories in the phase space, demonstrating high accuracy in capturing the underlying dynamics. The proposed framework provides a consistent and interpretable approach for frequency domain system identification in fractional-order nonlinear systems, with relevance to applications such as mechanical vibration analysis, structural health monitoring, and smart material modeling.
Continuum-type constitutive relations of odd matter need to be formulated according to the second law of thermodynamics. Based on the primitive thermodynamics of Edelen, a procedure admitting most general relations, is outlined for heat-conducting fluids and solids. For viscous responses of odd matter, the theory accounts for the irreversible and non-dissipative forces, besides the hyperdissipative ones. For quasi-static responses, the theory grasps the elastic and non-conservative forces besides those derivable from the free energy, this being the realm of Cauchy elasticity beyond hyperelasticity. In Cosserat-type odd matter, primitive thermodynamics also accounts for curvature-torsion and couple-stress besides, respectively, deformation and force-stress tensors. In both, classical and micropolar cases, the theory grasps all possible couplings between the thermodynamic velocity and force vectors, along with a full range of anisotropies of hyperdissipative and hyperelastic responses (both linear and nonlinear).
In order to quantitatively describe the influence of aggregate distribution on crack development and peak stress of recycled aggregate concrete, a multifractal spectrum theory was proposed to quantitatively characterize aggregate distribution in specimens. A mesomechanical model of reclaimed aggregate concrete mixed with natural aggregate and artificial aggregate was constructed. Numerical simulation tests were conducted on the uniaxial compression mechanical behavior of 25 groups of sample models with the same proportion and different aggregate distribution forms. Based on the box dimension theory, the multiple fractal spectrum method was used to quantitatively characterize the aggregate distribution form, and the key factors affecting cracks were explored based on the gray correlation degree. The research results show that the aggregate distribution in recycled aggregate concrete has multifractal characteristics. The multifractal spectrum was used to effectively characterize the aggregate distribution pattern, which can enlarge local details and provide new ideas for the quantitative analysis of the damage mode of recycled concrete. Secondly, by establishing a statistical model of the correlation between the multifractal spectrum width of the aggregate distribution pattern and the crack distribution box dimension, it was found that there was a positive correlation between the two, that is, the greater the multifractal spectrum width of the aggregate distribution pattern, the greater the crack box dimension, and the more complex the crack distribution. The complexity of aggregate distribution is closely related to the irregularity and complexity of mesoscopic failure crack propagation in recycled concrete specimens. In addition, gray correlation theory was applied to analyze the key factors affecting the formation of cracks in the specimens. The results showed that aggregate distribution had a first-order correlation with crack formation, and changes in aggregate distribution were an important factor affecting the performance of recycled concrete. Secondly, the poor mechanical properties of NAITZ led to obvious material damage, while NCA and MZ had a significant impact on the skeleton effect in the stress–strain process due to their large areas. This study deepens people’s understanding of the damage characteristics and cracking failure modes of recycled concrete. The study verifies the feasibility of the application of recycled aggregates and provides a valuable reference for engineering practice.