Search Results (275)

The present paper addresses models of non-local materials and, in particular, flexoelectric materials as dielectrics with higher-order gradients. While the literature develops the subject through variational formulations, here the modelling is developed within a thermodynamic framework with a general form of the Clausius–Duhem inequality, where the extra-entropy flux and the entropy production are given by constitutive functions. Furthermore, the polar character of the material, associated with flexoelectricity, is modelled by a body couple and no use is made of hyper-stresses. As a result of the thermodynamic analysis, it follows that the symmetric part of the stress and the electric polarization are given by a variational derivative of the electric enthalpy along with the dissipative parts that involve the selected function of entropy production. The skewed part of the stress is shown to be free from thermodynamic restrictions and is simply required to counterbalance the body couple. Full article

Diffusion against a concentration gradient, also called uphill transport, has been reported for magnesium and sulfate ions in solutions of NaCl and Mg${\mathrm{SO}}_4$ in reverse electrodialysis (RED). Here we derive transport equations for such systems and explain the observed uphill transport using non-equilibrium thermodynamics (NET). A set of Nernst–Planck equations was reformulated into a set of flux equations with neutral salt driving forces. By applying the condition of entropy production invariance to the sets of variables, we show how an ideal ion selectivity model provides Onsager coupling coefficients for the ion transport. These coupling coefficients can predict and explain the observed uphill transport of magnesium and sulfate. A linear fitting scheme is developed to fit the transport coefficients to experimental data for the ideal ion selectivity model and for a more general model. The results show that even the simplest ideal ion selectivity model captures the uphill transport, and the phenomenon occurs due to diffusional ion exchange, as in Donnan dialysis. Under open-circuit conditions, deviations are large, and the simplest model is no longer sufficient; co-ion leakage corrections are essential. The results provide a basis for future modelling of RED processes; in particular, one can determine and optimise the process efficiency, as the model gives direct access to the process’s local entropy production. Osmosis is identified as a potential source of error. Full article

We develop a KvN/Weyl/Wigner/Moyal phase-space formulation for shock-containing compressible, irrotational, barotropic Euler flow. Smooth branches are represented by branchwise Wigner distributions, while piecewise-smooth entropy-admissible shocks generate an interface-supported defect in the weak phase-space balance. This defect is concentrated on the moving shock surface and is weighted by the normal relative transport flux between the one-sided branches. An exact planar constant-state three-dimensional example shows how the same mass flux is transferred between distinct velocity-space supports and how its moments recover the classical jump structure. We also introduce a shock solution of the one-dimensional Burgers equation with a triangular initial profile as an exactly solvable reduced benchmark. In this example, the shock trajectory, transported branch weights, branchwise Wigner transforms, and a two-component localized phase-space defect are obtained in closed form. The construction is a restricted branchwise representation of Euler shocks already selected by the Rankine–Hugoniot and entropy conditions; it is not a new admissibility criterion or a complete global Wigner theory across discontinuities. The formulation separates smooth phase-space evolution from singular interface contributions within a unified construction and provides a compact diagnostic description of shock-supported phase-space structure. Full article

We present a machine learning approach for developing subgrid-scale (SGS) parameterizations in coarse simulations of partial differential equations. We utilize structure-preserving neural networks and entropy variables to learn subgrid fluxes in coarse simulations of the Burgers’ equation. In particular, we employ a decoupled neural network architecture explicitly separating the subgrid corrections into two distinct components: a conservative Flux Potential network and an Eddy Viscosity network. We demonstrate that this reduced-order framework maintains high physical fidelity, accurately reproducing the energy spectrum, spatial and temporal correlation functions, and dynamical characteristics of the full-scale system. Furthermore, we show that our approach is robust and applicable to parameters outside the training regime. Full article

The dynamic evolution of an optically induced vortex flow in nematic microliter droplets caused by exposure to a focused laser beam has been studied both experimentally using polarized optical microscopy and numerically within the framework of a corresponding nonlinear extension of the Ericksen–Leslie theory supplemented by thermomechanical correction of the stress tensor and the entropy balance equation. The vortex flow in nematic droplets consisting of 4-pentyl-4′-cyanobiphenyl molecules spreading over the functionalized surface was visualized in microliter droplets doped with monodisperse polystyrene tracers, under exposure to a laser beam with an optical power equal to 8.0 mW. Using the computer vision detection algorithm, we have identified radial symmetry in the tracers motion, where comet-like tracks are aligned along the rays emanating from the center of the resulting structure. At the same time, some of the “comets” are flying towards the center, while others are moving away from it. This allowed us to estimated the average value of tracer flows, which is of 17 µm/s. All these observations indicate that vortex currents are excited in the droplet under the action of the focused laser beam. The nature of thermally excited vortex flows in the microliter hybrid aligned nematic droplet with a free upper LC/air interface and spreading over the solid surface under the influence of the heat flux directed through the lower bounding surface is also numerically investigated. It was shown that due to the interaction between $\nabla T$ and the gradient of the director field $\nabla \widehat{\mathbf{n}}$, the thermally driven bi-vortical flow is maintained in nematic microvolume. Full article

The quantum measurement problem separates into operational questions: which observables are stable records, how outcome probabilities are represented, how conditional post-event states are updated, and how a detector event time is assigned. We give a compact architecture-conditional framework. In a finite-dimensional detector model, the detector-side relative-entropy flux is differentiated with the exact Fréchet derivative of the matrix logarithm. A noise-regularised timing distribution is defined and, under an explicitly assumed isolated non-degenerate maximum of the calibrated flux, Laplace asymptotics proves concentration at that maximum. Under stated fixed-point and detailed-balance hypotheses, the centre of the fixed-point algebra gives a canonical commutative record algebra. Outcome probabilities admit a POVM representation, and conditional updates use a completely positive (CP) instrument in its standard sense: CP maps whose traces give probabilities and whose normalised outputs give post-event states, summing to a trace-preserving map. Separately, an assumed modular-invariant inclusion of von Neumann algebras admits a state-preserving conditional expectation and CP retraction. A conditional quantum-error-correction lemma bounds accumulated record failure. These results do not derive unique outcomes from unitarity, construct a black-hole algebra inclusion, or resolve the black-hole information problem; they give a conditional framework, a worked illustration, and testable timing and record-stability criteria. Full article

This paper presents a comprehensive theoretical derivation of a membrane potential formula based on the Association-Induction Hypothesis (AIH), challenging traditional membrane theory and the Goldman–Hodgkin–Katz equation (GHK equation). The study demonstrates that membrane potential is not primarily a result of transmembrane ion transport through channels and pumps, but rather a consequence of the Boltzmann distribution of mobile ions influenced by their adsorption onto cell constituents. By employing a variational principle to minimize the total free energy of the system—consisting of ion mixing entropy, electrostatic energy, and adsorption energy—the authors derive a generalized membrane potential formula. Unlike the GHK equation, this model explicitly incorporates fixed charge density and the specific adsorption affinity of ion species such as $K^{+}$ and $N{H}_3^{+}$ onto carboxyl ($CO{O}^{-}$) groups. The derivation shows that cell potential (so-called membrane potential) can be generated even in the absence of a plasma membrane, suggesting that the transmembrane ion transport mediated by channels and pumps may not be the principal cause of the membrane potential generation but rather that the ion adsorption and desorption must govern the membrane potential generation. Ultimately, this research suggests that the fundamental mechanism of potential generation in biological systems is the equilibrium distribution of ions governed by thermodynamic stability rather than non-equilibrium steady-state flux. Full article

Water and nitrogen management influences farmland productivity and greenhouse gas emissions by regulating the soil micro-environment. However, the synergistic optimization strategy among yield improvement, economic benefit, and emission reduction in intercropping systems in arid regions remains unclear. Based on a two-year field experiment using an intercropping system of wolfberry and alfalfa, this study established four irrigation levels [full irrigation (W0), mild water deficit (W1), moderate water deficit (W2), and severe water deficit (W3)] and four nitrogen application levels [0 (N0), 150 (N1), 300 (N2), and 450 kg·ha⁻¹ (N3)]. The effects of water and nitrogen regulation on soil hydrothermal conditions, greenhouse gas emissions, crop yield, and economic benefits were systematically analyzed. The results showed that soil water content increased with higher nitrogen application rates but decreased with a more severe water deficit. In contrast, soil temperature exhibited the opposite trend, with the W3 treatment increasing by 2.23–2.41 °C compared to W0 during the full fruiting period. The emission fluxes of CO₂ and N₂O increased with higher nitrogen application rates but decreased with a more severe water deficit. CH₄ acted as a sink, with its uptake decreasing as nitrogen application increased and the water deficit intensified. CO₂ was the dominant contributor to the global warming potential of the intercropping system of wolfberry and alfalfa, accounting for 85.3–94.6% of the total. The emission fluxes of CO₂ and N₂O were significantly positively correlated with the soil water content, while the CH₄ emission flux was significantly positively correlated with the soil temperature. The W0N2 treatment achieved the highest system yield and net profit, whereas the W1N2 treatment exhibited the highest return on investment. A comprehensive evaluation using the entropy weight–TOPSIS model identified W1N2 as the optimal treatment. An integrated water–nitrogen decision model determined that the optimal water and nitrogen combination for achieving a high yield, a high efficiency, and low emissions was an irrigation amount of 4245–4413 m³·ha⁻¹ and a nitrogen application rate of 290–323 kg·ha⁻¹. The findings of this study can provide a scientific basis for the sustainable water and nitrogen management of characteristic cash crop intercropping systems in arid regions. Full article

Compared with straight microchannels, wavy microchannels have been shown to significantly improve the heat transfer capability of microchannel heat sinks. The present study introduces a bidirectional curved wavy microchannel design aimed at enhancing performance. The thermo-hydraulic performance of bidirectional curved and ordinary wavy microchannels within the Reynolds number range of 300–800 is analyzed numerically under a constant heat flux. The results indicate that the bidirectional curved microchannel achieves optimal performance at an inlet velocity of 0.6 m/s. Compared with the ordinary wavy microchannel, the comprehensive performance factor of the bidirectional curved wavy microchannel with A₂ = 2 mm and λ₂ = 8 mm increases by 48% under the same inlet Reynolds number. For the preferred bidirectional curved wavy microchannel with A₂ = 2 mm and λ₂ = 12 mm, the average secondary flow intensity is enhanced by 153%, the comprehensive performance factor reaches 1.35, and the minimum entropy generation rate decreases by 6.87%. The enhanced heat transfer is attributed to the increased main flow velocity and the secondary flow intensity due to the bidirectional curve, which promotes coolant mixing. Full article

Canned motor pumps are widely utilized due to their distinct advantage of a completely leakage-free structure. Among them, an integrated impeller–rotor configuration is employed in the axial-flux canned motor pump, resulting in a shorter axial length and higher power density. This novel configuration allows for easy integration into space-constrained systems, such as electric vehicles, aerospace applications, and liquid-cooled servers. However, research on the internal flow characteristics of these pumps remains scarce. To address this gap, the present study investigates the internal flow across various flow rates. Numerical simulations are validated against experimental data. The average error remains below 2%. The pump achieves a peak efficiency of 68.6% at the design condition, but experiences efficiency drops of 15.0 and 25.2 percentage points under 0.5Q_d and 1.5Q_d, respectively. Results demonstrate that flow rates significantly govern internal characteristics. These include pressure, velocity, and entropy distributions, along with vortex structures and pressure fluctuations. Notably, operating at off-design conditions can intensify the internal pressure fluctuations by up to a factor of 29.4. Entropy analysis identifies major losses on blade suction sides and diffusers. These findings provide crucial hydrodynamic guidelines for low-noise thermal management systems in electric vehicles and ensuring high-reliability cooling loops in aerospace and liquid-cooled servers. Full article

Hybrid carbon nanotube–fullerene architectures provide a controllable setting in which to study irreversibility and information flow in strongly structured quantum environments. We analyze entropy generation in a platform where paramagnetic endohedral fullerenes (PEFs), such as N@C₆₀ and P@C₆₀, are encapsulated inside a suspended carbon nanotube (CNT) resonator, such that selected multi-level PEF spin states define an effective qubit coupled to quantized CNT flexural modes. Motivated by prior work on fullerene-filled CNTs, on spin–phonon manipulation in suspended nanotubes, and on exact phase-space propagators for damped driven oscillators, we formulate a hybrid open-system description that combines a driven quantum Brownian description of the CNT resonator with an effective Jaynes–Cummings type spin–vibrational interaction. The resonator dynamics are represented in phase space through the Wigner function, whose time evolution can be written analytically in terms of the initial Wigner distribution and a Gaussian propagator. This representation makes it possible to separate drive-induced phase space displacement, diffusion, and damping, and to connect these features directly to entropy flow. The coupled spin–mechanical dynamics are then embedded in a Lindblad quantum master equation that includes mechanical damping, spin relaxation, pure dephasing, and thermally activated excitation channels. Within this framework we derive the entropy balance equation—identifying entropy flux and non-negative entropy production—and examine how hybridization between the molecular spin and the nanotube vibration redistributes irreversibility between coherent exchange and dissipative channels. We show that spin–phonon coupling enhanced by a magnetic field gradient, resonant driving, and moderate thermal occupation can produce identifiable crossovers between entropy–production regimes dominated by the oscillator and those dominated by the spin. The resulting framework provides a quantitative basis for using CNT–PEF hybrids as nanoscale platforms for studying nonequilibrium quantum thermodynamics, decoherence, and information loss in structured vibrational environments. Full article

We investigatewhether a finite local information capacity of spacetime can account for the gravitational phenomena commonly attributed to cold dark matter. Starting from a covariant effective-field-theory description, we modelcoarse-grained entropy deposition as a dynamical scalar field $S\left(x\right)$ whose stress–energy tensor contributes to structure formation. The macroscopic action contains a single dimensionless coupling λ multiplying the canonical kinetic term, ensuring ghost-free dynamics and conservation of the associated stress–energy tensor. In a slow-roll regime, defined by a covariant source term $\Gamma \equiv \ddot{S}+3H\dot{S}=0$, where H is the Hubble parameter and overdot denotes derivative with respect to cosmic time, and $|\ddot{S}|\ll H|\dot{S}|$, the entropy sector behaves as pressureless dust at background and in linear order. Implemented in a modified Cosmic Linear Anisotropy Solving System (CLASS) Boltzmann solver, the entropy component fits Planck satellite 2018 cosmic microwave background (CMB) data, baryon acoustic oscillation (BAO) measurements, and the Pantheon + Type Ia supernova sample for $0.5\lesssim \lambda \lesssim 2$, while preserving the linear growth factor to within 0.2% over Euclid space telescope scales. To regulate ultraviolet contributions, we introduce a holographically motivated prescription in which gravitationally active entropy deposition is confined to causal two-surfaces, yielding a $\rho \propto r^{-2}$ halo envelope with a finite-density core determined by local entropy saturation. Fixing the flux scale $\mathcal{A}$ from astrophysical entropy budgets reproduces Milky-Way-mass halos without introducing fine-tuned length scales. Pilot N-body simulations that evolve the entropy field on a staggered grid reproduce the halo mass function down to ${10}^{10.5}{M}_{\odot }$, mitigate the cusp–core and missing-satellite tensions, and remain consistent with cluster lensing constraints. On linear scales, the model predicts percent-level, scale-dependent deviations in the lensing convergence and matter power spectra, testable by Euclid space telescope, the Roman Space Telescope High Latitude Survey, and the CMB-S4 experiment. Full article

The attribution of systemic financial stress to specific market sectors requires metrics that are faithful to the model’s computations, statistically consistent, and connected to a physically meaningful measure of directed information flow. This paper addresses all three requirements through information geometry, contributing to SDGs 7, 8, 9, and 17 through an entropic causal chain linking energy infrastructure failure to financial market stress. We conjecture and empirically verify the Entropy–Saliency Equivalence: Metabolic Saliency is an asymptotically unbiased estimator of the local Kullback–Leibler divergence between stressed and resting sector return distributions, with bias decaying at a parametric rate under Gaussian regularity conditions. The finite-sample bias–variance decomposition of the Kraskov–Stögbauer–Grassberger transfer entropy estimator is derived, establishing a minimax-optimal convergence rate. A novel metric, the Spatio-Temporal Information Flux (STIF), quantifies directed inter-sector stress transmission in bits per trading day, providing a bootstrap-calibrated audit trail aligned with the South African Financial Sector Regulation Act and MiFID II. Empirical validation on the JSE canonical panel (87 securities, 2857 trading days, 2015–2026) with Eskom load-shedding stages as exogenous stress injectors confirms the equivalence ($R^2=0.810$, $\widehat{\rho }=0.90$), with walk-forward $R^2=0.789$ and placebo $R^2=0.081$ ruling out estimation artefacts. The energy sector is identified as the primary stress transmitter during Stage 4+ Eskom events (STIF rising from 0.14 to 0.43 bits/day, directional asymmetry ratio 4.7). Robustness checks confirm stability across non-Gaussian securities and rolling transfer entropy windows. Full article

When the global energy transition is analyzed through economic lenses, the constraints imposed by the laws of thermodynamics are often overlooked. This study addresses the Latecomer’s Dilemma—the predicament of semi-peripheral nations compelled to decarbonize without the capital stock accumulated following the example of the countries of the Global North during their more than two hundred years of industrial development associated with the saturation of the atmosphere with carbon dioxide. A novel phase space model of the Anthropocene is constructed, synthesizing the political concept of ecological debt with the biophysical reality of entropy debt. The application of the laws of systems ecology and non-equilibrium thermodynamics enables the mapping of national development trajectories against the saturated “atmospheric bathtub”. The analysis identifies a critical Injustice Gap—a region of phase space physically foreclosed by historical emissions. Moreover, it has been demonstrated that a circular economy powered by low-density renewables functions as an entropy trap, converting material debt into radiative debt without achieving a closed loop. Consequently, the Polish correction vector is proposed as a stabilization mechanism. This study’s findings indicate that addressing the emerging phenomenon of adaptation apartheid necessitates the implementation of a high-density energy flux, namely Generation IV nuclear reactors, which would be funded by a retroactive ETS3 mechanism. This approach fulfills the thermodynamic condition for material closure, thereby substantiating the notion that energy justice constitutes a physical necessity for planetary stability. This study quantifies the historical radiative debt of a single early-industrialized hub (Manchester) at approximately 142.8 billion EUR. The novelty lies in the synthesis of biophysical laws and the Latecomer’s Dilemma through the proposed ETS3 mechanism. Full article

This communication discusses the problem of depositing equiatomic metal alloy films. It is shown that this problem can be solved using a magnetron equipped with a target constructed using a new “multilayer target” paradigm. This target, sputtered in an argon environment, consists of several parallel metal plates mounted on the magnetron axis. A method based on the equality of the sputtered fluxes generated by the plates is proposed for calculating the geometric dimensions of the plates. This equality leads to a system of algebraic equations, which are proposed to be solved under the assumption of a uniform discharge current density distribution in the sputtering region of the target. The communication describes two types of targets in which the plates have slots of different shapes. In one case, the slots are shaped as sectors of a ring with a given angle. In the other, the plates are shaped as rings. As examples, the geometric dimensions of targets for a balanced magnetron system intended for the deposition of films of equiatomic Ti_0.33Ta_0.33Nb_0.33 and Ti_0.25Ta_0.25Nb_0.25Mo_0.25 alloys are calculated. The presentation is accompanied by the results of individual experiments. This report is preliminary in nature; experimental verification is ongoing. The application of the new paradigm in magnetron target design facilitates the fabrication of films of nanostructured medium- and high-entropy alloys with specified chemical compositions, which is the central theme of the Special Issue devoted to functional nanomaterials. Full article