Equilibrium Of System Research Articles

Radiative heat transfer (RHT) at the nanoscale can vastly exceed the far-field blackbody limit due to the tunneling of evanescent waves, a phenomenon traditionally described by fluctuational electrodynamics (FE). While FE has been exceptionally successful for systems in local thermal equilibrium, its foundational assumptions break down in the growing number of scenarios involving genuine non-equilibrium conditions, such as in active devices or driven materials. This review introduces the non-equilibrium Green's function (NEGF) formalism as a powerful and versatile framework to study RHT beyond these classical limits. Rooted in quantum many-body theory, NEGF provides a unified language to describe energy transport by photons, electrons, and phonons on an equal footing. We first outline the theoretical foundations of the NEGF approach for RHT, demonstrating how it recovers the canonical results of FE in the local equilibrium limit. We then survey recent breakthroughs enabled by NEGF, including: (i) providing a quantum-accurate description of equilibrium RHT that naturally incorporates non-local and finite-size effects, resolving unphysical divergences predicted by local models; (ii) unifying heat transfer channels to reveal the non-additive synergy between radiation, electron tunneling, and phonon conduction at sub-nanometer gaps; (iii) enabling the quantum design of materials and metamaterials with tailored thermal properties through band structure and topological engineering; and (iv) describing active control of heat flow in driven systems, which allows for phenomena like isothermal heat transfer and pumping heat against a temperature gradient. By shifting the paradigm from passive analysis to active control and design, the NEGF formalism opens a new frontier for manipulating thermal energy at the nanoscale, with profound implications for thermal management, energy conversion, and thermal information processing.

Integrated experimental and thermodynamic modelling study of phase equilibria in the “CuO0.5”-PbO-AlO1.5 system in equilibrium with Cu/Pb metal

Radiative cooling is a sustainable alternative to conventional vapor compression-based systems. However, achieving subfreezing temperatures remains a significant challenge particularly in humid environments where a strong atmospheric back-radiation and parasitic heat transfer often necessitate the use of vacuum chambers. Angular-selective thermal emission has been proposed as a strategy to mitigate radiative heat gain from the atmosphere. Nevertheless, a fundamental drawback of employing thermal emission selectivity, whether spectral or angular, is the accompanying reduction in the emitter's total radiated power which diminishes the emitter's ability to overcome environmental heating. In this work, we investigate the use of angular shields to introduce angularly selective thermal emission without reducing the emitter's radiated power. We analyze the effects of spectral selectivity, humidity, and parasitic heating on the system's net radiative flux and equilibrium temperature. Our analysis shows that spectrally selective thermal emission is necessary for efficient cooling. While engineered angular emission outperforms angular shields under high humidity, angular shields outperform in scenarios with parasitic heating, owing to their preservation of the emitter's omnidirectional emission. Angular shielding can enable subfreezing temperatures with simple insulation when the average atmospheric transmittance exceeds 70%.

Mass-balanced compartmental systems defy classical deterministic entropy measures since both metric and topological entropy vanish in dissipative dynamics. By interpreting open compartmental systems as absorbing continuous-time Markov chains that describe the random journey of a single representative particle, we allow established information-theoretic principles to be applied to this particular type of deterministic dynamical system. In particular, path entropy quantifies the uncertainty of complete trajectories, while entropy rates measure the average uncertainty of instantaneous transitions. Using Shannon’s information entropy, we derive closed-form expressions for these quantities in equilibrium and extend the maximum entropy principle (MaxEnt) to the problem of model selection in compartmental dynamics. This information-theoretic framework not only provides a systematic way to address equifinality but also reveals hidden structural properties of complex systems such as the global carbon cycle.

Far from equilibrium, chemical and biological systems can form complex patterns and waves through reaction-diffusion coupling. Fluid motion often interferes with these self-organized concentration patterns. This study examines the influence of Marangoni-driven flows inside a thin layer of fluid ascending the outer surfaces of hydrophilic obstacles on the spatio-temporal dynamics of chemical waves in the modified Belousov-Zhabotinsky reaction. These observations reveal that circular waves originate nearly simultaneously at the obstacles and propagate outward. In a covered setup, where evaporation is minimal, the wavefronts maintain their circular shape. However, in an uncovered setup with significant evaporation and resulting Marangoni flows, the interplay between surface tension-driven Marangoni flows and gravity destabilizes the wavefronts, creating distinctive flower-like patterns around the obstacles. Experiments further show that the number of petals increases linearly with obstacle diameter, though a minimum diameter is required for these instabilities to appear. Our complementary numerical analysis indicates that solutal Marangoni forces dominate thermal ones in this system. These findings demonstrate the potential to "engineer" specific wave patterns, offering a method to control and direct reaction dynamics. This capability is especially important for developing microfluidic devices requiring precise control over chemical wave propagation.

Gaussian fluctuations are intrinsic to systems in thermal equilibrium and are also a tenet of near-equilibrium systems related by linear response. We recently introduced a Gaussian (fluctuation) approximation to demonstrate that the entropy production rate and power dissipation are equal to each other in multiparticle overdamped nonconservative nonequilibrium systems. The fluctuations of the nanoparticle constituents of the optical matter (OM) systems studied, characterized through their collective modes of motion, satisfied the Gaussian approximation. Here, we report a type of collective mode and motion in a different OM system that manifests strong non-Gaussian behavior. We show through experiments and simulations that the collective motion is a pseudorotation of the overdamped and nonconservative 8-silver-nanoparticle OM structure in water. The OM system has D2 point group symmetry (in 2-dimensional space) and exists in a nonequilibrium steady state (NESS) at various temperatures and solution ionic strengths. We developed a weighted principal component analysis (w-PCA) and state-free nonreversible VAMPnet (Variational Approach to Markov Process solved via neural network) method to identify the collective modes of the nanoparticle motion and the time scales of their dynamics, including pseudorotation. We show that the confinement exerted by the outer four particles on the inner four particles has a significant temperature-dependent impact on the pseudorotation dynamics. We attribute the counterintuitive change of the dynamics with increasing temperature─changing from monomodal Gaussian-like to bimodal with the same mean─to the implicit nature of the interparticle interactions and resultant forces. The nonconservative force field determined at each time step of our simulations is an intrinsic characteristic of these nonequilibrium many-body interacting OM systems. We anticipate that our w-PCA+VAMPnet method will be useful in studies of collective motions of complex overdamped and nonconservative systems, and of particle dynamics in other systems such as cluster liquids (e.g., liquid sulfur).

ABSTRACTIn this work, we introduce a mathematical model for diabetes that uses time‐delay and variable‐order fractional derivatives, aiming to better reflect the complex and memory‐dependent behavior of glucose and insulin dynamics. The model is built using the Caputo definition of variable‐order derivatives. We explore the system's equilibrium points and examine their stability to understand how the system's behavior changes with different parameters. We also study the positivity and boundedness of the proposed system. To solve the model numerically, we design an effective method that combines a nonstandard finite difference scheme with the Grünwald–Letnikov operator. We analyze the proposed scheme and prove that the approximated solutions remain nonnegative and bounded. Through numerical simulations and comparisons, we demonstrate the reliability and practical advantages of our approach. The results highlight the crucial impact of time‐delay and variable‐order fractional dynamics on diabetes progression and treatment. Delayed insulin response and memory effects in glucose–insulin interaction are effectively modeled. This enhances the realism and personalization of blood sugar regulation analysis.

ABSTRACTAccurate parameter estimation in vapor–liquid equilibrium (VLE) systems is essential for reliable process simulation and design, particularly in systems involving biodiesel‐related compounds. This study investigates the effect of temperature on model accuracy by incorporating temperature dependence in the Wilson model through two variants: the classical Wilson‐I (temperature‐independent) and the extended Wilson‐II (temperature‐dependent) models. A comparative analysis is conducted using three evolutionary algorithms—classical differential evolution (DE), opposite point‐based DE (OPDE), and the improved OPDE (IOPDE)—under both least‐squares (LS) and error‐in‐variable (EIV) approaches. Fourteen isobaric systems relevant to biodiesel production are analyzed, and a merged dataset for the methyl palmitate (1) + methyl stearate (2) system is introduced to assess model robustness across a wider composition and pressure range. Results show that while the LS approach converges faster, the EIV method provides superior prediction accuracy. The Wilson‐I model generally yields better agreement with experimental data; however, the Wilson‐II model demonstrates enhanced accuracy in selected problems and for the merged dataset due to its consideration of temperature effects. The IOPDE algorithm consistently achieves a 100% success rate with a significantly lower number of function evaluations (NFEs), outperforming DE and OPDE in all cases. Overall acceleration rate (AR) analysis further confirms its computational efficiency and robustness. This work demonstrates that the IOPDE‐EIV combination offers a highly effective optimization framework for thermodynamic parameter estimation, with improved fidelity in temperature‐sensitive VLE modeling of biodiesel systems.

Predicting the binding affinity of ligands to protein pockets is key in the drug design pipeline. The flexibility of ligand-pocket motifs arises from a range of attractive and repulsive electronic interactions during binding. Accurately accounting for all interactions requires robust quantum-mechanical (QM) benchmarks, which are scarce for ligand-pocket systems. Additionally, disagreement between “gold standard” Coupled Cluster (CC) and Quantum Monte Carlo (QMC) methods casts doubt on many benchmarks for larger non-covalent systems. We introduce the “QUantum Interacting Dimer” (QUID) benchmark framework containing 170 non-covalent (non-)equilibrium systems modeling chemically and structurally diverse ligand-pocket motifs. Symmetry-adapted perturbation theory shows that QUID broadly covers non-covalent binding motifs and energetic contributions. Robust binding energies are obtained using complementary CC and QMC methods, achieving agreement of 0.5 kcal/mol. The benchmark data analysis reveals that several dispersion-inclusive density functional approximations provide accurate energy predictions, though their atomic van der Waals forces differ in magnitude and orientation. Contrarily, semiempirical methods and empirical force fields require improvements in capturing non-covalent interactions (NCIs) for out-of-equilibrium geometries. The wide span of NCIs, highly accurate interaction energies, and analysis of molecular properties take QUID beyond the “gold standard” for QM benchmarks of ligand-protein systems.

Purpose This study proposes a non-smooth static analysis method for tensegrity structures to address the issue of slack cables in nonlinear deformation. Slack cables introduce discontinuities in structural behavior, causing instability in numerical computations. Design/methodology/approach The static equilibrium system is reformulated as a linear complementarity problem (LCP), ensuring stability even in structures with numerous slack cables. An index matrix is used to reduce the system dimension by eliminating fixed degrees of freedom, while a dynamic step size strategy based on the structure’s total potential energy improves convergence. Findings Several numerical examples demonstrate that the stability of the solution is improved, especially in systems with a large number of slack cables. Moreover, the equilibrium equations are simplified to involve only the degrees of freedom of free nodes, which enhances computational efficiency. Originality/value The proposed method allows for static analysis of any prestressed tensegrity structure within an acceptable error range and provides a theoretical formulation for slack cables in the structure.

We propose a universal framework for understanding system evolution based on structural complexity, offering a directional signature that applies across physical, chemical, and biological domains. Unlike entropy, which is constrained by its definition in closed, equilibrium systems, we introduce Kolmogorov Complexity (KC) and Fractal Dimension (FD) as quantifiable, scalable metrics that capture the emergence of organized complexity in open, non-equilibrium systems. We examine two major classes of systems: (1) living systems, revisiting Schrödinger’s insight that biological growth may locally reduce entropy while increasing structural order, and (2) irreversible natural processes such as oxidation, diffusion, and material aging. We formalize a Universal Law: expressed as a non-decreasing function Ω(t) = α·KC(t) + β·FD(t), which parallels the Second Law of Thermodynamics but tracks the rise in algorithmic and geometric complexity. This framework integrates principles from complexity science, providing a robust, mathematically grounded lens for describing the directional evolution of systems across scales-from crystals to cognition.

The Reactivity of α‐Fluorinated Mono‐ and Diketones Uncovers their Potential as Electrophilic Warheads for Reversible Covalent Drugs

Homogeneous nucleation, a textbook transition path for phase transitions, is typically understood on thermodynamic grounds through the prism of classical nucleation theory. However, recent studies have suggested the applicability of classical nucleation theory to systems far from equilibrium. In this article, we formulate a purely mechanical perspective of homogeneous nucleation and growth, elucidating the criteria for the properties of a critical nucleus without appealing to equilibrium notions. Applying this theory to active fluids undergoing motility-induced phase separation, we find that nucleation proceeds in a qualitatively similar fashion to equilibrium systems, with concepts such as the Gibbs-Thomson effect and nucleation barriers remaining valid. We further demonstrate that the recovery of such concepts allows us to extend classical theories of nucleation rates and coarsening dynamics to active systems upon using the mechanically derived definitions of the nucleation barrier and surface tensions. Three distinct surface tensions-the mechanical, capillary, and Ostwald tensions-play a central role in our theory. While these three surface tensions are identical in equilibrium, our work highlights the distinctive role of each tension in the stability of active interfaces and the nucleation and growth of motility-induced phases.

We report the experimental observation of a square crystalline phase in a vibrated binary mixture of spherical grains. This structure spontaneously forms from a disordered state, consistently with predictions obtained in an equilibrium system with similar geometrical properties under conservative dynamics. By varying the area fraction, we also observe stable coexistence between a granular fluid and an isolated square crystal. Using realistic simulations based on the discrete element method and an idealized collisional model integrated via event-driven molecular dynamics, we not only reproduce experimental results but also help to gain further insights into the non-equilibrium phase coexistence. Through the direct phase coexistence method, we demonstrate that the system shows behavior highly similar to an equilibrium first-order phase transition. However, the crystal remains at a higher granular temperature than the fluid, which is a striking non-equilibrium effect. Through qualitative arguments and supported by kinetic theory, we elucidate the role of the coupling between local structure and energy transfer mechanisms in sustaining kinetic temperature gradients across the fluid-solid interface.

Optimal control strategies for mitigating antibiotic resistance: Integrating virus dynamics for enhanced intervention design.

Towards a Possible Definition of Consciousness.

Path planning algorithms for mobile robots and autonomous systems have advanced considerably, yet challenges remain in navigating complex environments while satisfying non-holonomic constraints and achieving precise target orientation. Phase portraits are traditionally used to analyse dynamical systems via equilibrium points and system trajectories, and can be a powerful framework for addressing these challenges. In this work, we propose a novel orientation-aware path planning algorithm that uses phase portrait dynamics by treating both obstacles and target poses as equilibrium points within the environment. Unlike conventional approaches, our method explicitly incorporates non-holonomic constraints and target orientation requirements, resulting in smooth, feasible trajectories with high final pose accuracy. Simulation results across 28 diverse scenarios show that our method achieves zero final orientation error with path lengths comparable to Hybrid A*, and planning times reduced by 52% on the indoor map and 84% on the playpen map relative to Hybrid A*. These results highlight the potential of phase portrait-based planning as an effective and efficient method for real-time autonomous navigation.

The integration of evolutionary models with economic theory offers a robust mathematical framework for understanding financial instability, market bubbles and fiscal crises. Some models often fail to capture the complexity of financial breakdowns due to their reliance on linear and deterministic assumptions. In contrast, the master equation approach highlights the dominance of nonlinear and stochastic dynamics, demonstrating that economic collapses stem from systemic instabilities. By classifying financial crises into gradual decline, gradual constraints, abrupt collapse and cyclical crises, this approach provides a structured perspective on macroeconomic vulnerabilities. Bifurcation theory, stochastic jump processes and financial fragility hypotheses illustrate how small perturbations can trigger disproportionate systemic disruptions. The sudden shift in Greece’s sovereign debt crisis exemplifies the nonlinear transition from stability to crisis. These insights reinforce the need for adaptive economic models that incorporate real-time data and evolutionary dynamics. Policymakers can enhance financial resilience by designing early warning systems that detect bifurcation thresholds and implementing flexible regulatory mechanisms. Ultimately, embracing complexity and instability as inherent economic features will lead to more effective crisis management and policy interventions. Future research should integrate machine learning and advanced simulations to refine predictive accuracy and improve macroeconomic stability. JEL Codes: E32, E44, G01, G38, C63

Umm Al Quwain (UAQ) lagoon is a natural lagoon located in the northeastern part of the United Arab Emirates (UAE). Understanding the water circulation in the lagoon is essential for implementing the effective conservation measure to withstand future morphological changes. In this study, a two-dimensional hydrodynamics model is applied for UAQ lagoon using Delft3D-FM to investigate tide variability and currents within and on adjacent coastal lagoon region. The results show a maximum positive water level inside the lagoon of approximately 1.22 m relative to local mean sea level. Water levels within the vicinity of the lagoon range from − 0.95 to 1.22 m. Additionally, it was identified areas within the lagoon where currents increase up to 1.6 m/s due to the narrow inlet in the western entrances. However, most currents inside the lagoon are calmer varying from 0.1 to 0.4 m/s. The net residual currents indicate a system in equilibrium, as the import and export estimates are close to zero and can be considered negligible. The findings of this study provide a baseline study of the flow characteristics at UAQ lagoon and enable future broader research.

We investigate the response of a system of hard spheres to two classes of perturbations over a range of densities spanning the fluid, crystalline, and glassy regimes within a molecular dynamics framework. First, we consider the relaxation of a "thermal inhomogeneity," in which a central region of particles is given a higher temperature than its surroundings and is then allowed to evolve under Newtonian dynamics. In this case, the hot central "core" of particles expands and collides with the cold surrounding material, creating a transient radially expanding "compression wave," which is rapidly dissipated by particle-particle collisions and interactions with periodic images at the boundary, leading to a rapid relaxation to equilibrium. Second, we consider a rapid compression of the spheres into a disordered glassy state at high densities. Such rapidly compressed systems exhibit very slow structural relaxation times, many orders of magnitude longer than thermalization times for simple temperature inhomogeneities. We find that thermal relaxation of the velocity distribution is determined simply by the total collision rate, whereas structural relaxation requires coordinated collective motion, which is strongly suppressed at high density, although some particle rearrangement nevertheless occurs. We further find that collisions propagate significantly faster through glassy systems than through crystalline systems at the same density, which leads to very rapid relaxation of velocity perturbations, although structural relaxation remains very slow. These results extend the validity of previous observations that glassy systems exhibit a hybrid character, sharing features with both equilibrium and nonequilibrium systems. Finally, we introduce the hard-sphere causal graph, a network-based characterization of the dynamical history of a hard-sphere system, which encapsulates several useful metrics for characterizing hard-sphere systems within a single structure, and which emphasizes the role of causality in these systems.