Thermal-vibrational-activation-dominated hot-band absorption (HBA) is a key mechanism for achieving anti-Stokes luminescence, utilizing environmental thermal energy to enable photon emission at energies higher than absorption. The HBA necessitates thermal vibrational activation (υ = 0 → 1), which remains a challenging yet critical task in molecular design. This study presents a molecular design strategy integrating a multi-resonance core with tailored peripheral groups. Through the modification of the surrounding groups, the vibrational modes that contribute to the thermal vibrational activation can be modulated. The mechanism of the thermal vibrational activation is elucidated by distinguishing the roles of the resonance core and peripheral groups in governing low- and high-energy vibrational modes, respectively. Based on statistical mechanics, a theoretical approach is proposed to analyze the contribution of each vibrational mode. A structure-property relationship is established for HBA systems, providing a foundational framework for the development of advanced anti-Stokes luminescent materials.

Organisations increasingly combine social innovation and environmentally orientated technologies in response to sustainability and stakeholder pressures. However, empirical evidence remains limited on how organisational actors perceive and cognitively associate social innovation, green technologies, and practices related to the Sustainable Development Goals (SDGs), particularly in emerging European economies. This study addresses this gap by examining whether employees and managers perceive these dimensions as interconnected and whether green technologies represent a statistically significant indirect association between social innovation and SDG-related organisational practices. Using a cross-sectional online survey of 265 employees and managers from Romanian companies in production, services, IT, and commerce, we estimated an exploratory structural model through partial least squares structural equation modelling (PLS-SEM). The results reveal strong positive associations between perceived social innovation and SDG-related organisational practices, as well as between perceived social innovation and green technologies. Green technologies are also positively associated with SDG-related practices and exhibit a statistically significant indirect association within the observed pattern of associations. Consistent with perception-based research design, these findings suggest that respondents cognitively group social and technological initiatives as complementary components of a broader sustainability orientation, rather than indicating statistical or process-based mechanisms. The study contributes to organisational sustainability research by integrating social innovation and green technologies within a single organisational-level framework and by providing context-specific evidence from Romania, an under-represented central and Eastern European context.

Predicting fracture precursors in cementitious materials using natural time analysis coupled with non-extensive statistical mechanics

Clathrate hydrates are non-stoichiometric inclusion compounds with critical relevance to energy resources and CO2 sequestration, formed by guest molecules encapsulated in water cages. This perspective overviews the synergistic progress achieved through statistical mechanics and molecular simulation with intermolecular potential models in three key areas: thermodynamic stability, structural polymorphism, and dynamic processes. Theoretical estimation of its stability, originated from the van der Waals and Platteeuw theory, has been greatly improved by revisions accounting for constant pressure conditions, multiple occupancy, and host-guest coupling, enabling accurate prediction of multi-phase coexistence. Novel hydrate and ice structures have been synthesized using new strategies. The Frank-Kasper HS-I phase is unstable with small gas molecules, however, it was realized as a semiclathrate hydrate with an alkyl ammonium salt. We also discuss several possible strategies to form metastable ices, such as degassing of gas hydrates. The dynamic aspects have been investigated using molecular dynamics simulations. It was shown that dissociation kinetics are significantly influenced by guest concentration and bubble formation. Molecular dynamics simulations have also provided valuable insights into two types of low dosage hydrate inhibitors.

We construct dynamic models governing two nonreciprocally coupled fields for several cases with zero, one, and two conservation laws. Starting from two microscopic nonreciprocally coupled Ising models, and using the mean-field approximation, we obtain closed-form evolution equations for the spatially resolved magnetization in each lattice. Only allowing for single spin-flip dynamics, the macroscopic equations in the thermodynamic limit are closely related to the nonreciprocal Allen-Cahn equations, i.e., conservation laws are absent. Likewise, only accounting for spin-exchange dynamics within each lattice, the thermodynamic limit yields equations similar to the nonreciprocal Cahn-Hilliard model, i.e., with two conservation laws. In the case of spin-exchange dynamics within and between the two lattices, we obtain two nonreciprocally coupled equations that add up to one conservation law. For each of these cases, we systematically map out the linear instabilities that can arise. Moreover, combining the different dynamics gives a large number of further models. Our results provide a microscopic foundation for a broad class of nonreciprocal field theories, establishing a direct link between non-equilibrium statistical mechanics and macroscopic continuum descriptions.

Grafting has been practiced for millennia to combine the best characteristics of two plants. Despite recent molecular discoveries that gain insight into plant grafting, the systematic characterization of its underlying mechanisms is still lacking. Here, we take a step toward filling this gap by developing a generalized statistical mechanics model to decode genomic crosstalk between the scion and rootstock. Instead of traditional objectives of identifying individual genes that are differentially expressed between the two organs, our model codes thousands of interactive genes into informative, dynamic, omnidirectional, and personalized networks (idopNetworks) that program and rewire scion-rootstock crosstalk. We design an experiment of reciprocally micrografting young tissues to validate the application of idopNetworks to the genomic characterization of graft formation between two distantly related Populus species. Given its capacity to reveal the most comprehensive genomic underpinnings for proper interactions of the scion with rootstock to develop new plants, the idopNetworks model can be extended for the mechanistic exploration of a wide range of biological, evolutionary, and medical phenomena.

Abstract Dense associative memory (DAM) models have been attracting renewed attention since they were shown to be robust to adversarial examples and closely related to cutting edge machine learning paradigms, such as the attention mechanism and generative diffusion. We study a DAM built upon a three-layer Boltzmann machine with Potts hidden units, which represent data clusters and classes. Through a statistical mechanics analysis, we derive saddle-point equations that characterize both the stationary points of DAMs trained on real data and the fixed points of DAMs trained on synthetic data within a teacher-student framework. Based on these results, we propose a novel regularization scheme that makes training significantly more stable. Moreover, we show empirically that our DAM learns interpretable solutions to both supervised and unsupervised classification problems. Pushing our theoretical analysis further, we find that the weights learned by relatively small DAMs correspond to unstable saddle points in larger DAMs. We implement a network-growing algorithm that leverages this saddle-point hierarchy to drastically reduce the computational cost of training dense associative memory.

In atomic force microscopy (AFM), the detection of interactions between the probe tip and the sample surface is the basis of topography imaging. It is crucial to minimize the tip-sample interaction to prevent deformation or damage to soft biological macromolecules in AFM imaging. Here, a scanning mode of AFM was developed to image soft biological macromolecules with a sub-10 pN load force. In this scanning mode, the reduction in the thermal fluctuation of the cantilever was monitored at subnanometer tip-sample separations, where interaction with the sample begins to influence cantilever behavior. The height of the sample was controlled such that the magnitude of the thermal fluctuation of the cantilever remained constant. The magnitudes of the fluctuations and forces in this scanning mode were formulated within the framework of statistical mechanics. It was estimated that the repulsive force acting between the probe tip and sample surface originated largely from the entropic effect of the reduction in cantilever fluctuation. Two proteins (GroEL and bacteriorhodopsin) were imaged to demonstrate the capability of this scanning mode for acquiring topography with a marginal load force. The fragile double-ring structure of GroEL was preserved after repeated scans. The flexible C-terminal region of bacteriorhodopsin was clearly visualized. Thus, the presented AFM imaging mode is highly noninvasive for soft and fragile biological macromolecules.

Editorial: Special Issue on Nonequilibrium statistical mechanics: Methods, applications and new trends

Physics- and data-driven active learning of neural network representations for free energy density functions of materials from statistical mechanics

We present a machine-augmented molecular dynamics (MAMD) framework in which particle velocities are updated using predictions from stacked long short-term memory networks trained on historical velocity and coordinate data. MAMD propagates coordinate trajectories in time without access to forces or energies during training or inference. Applied to isolated harmonic diatomics, MAMD conserves total energy, preserves molecular structure, and reproduces velocity autocorrelation functions. Small integration errors can accumulate over long trajectories, but we show that molecular dynamics stability can be recovered through periodic, but infrequent injections of velocity updates computed from Hamiltonian forces (frequency ≤0.01). We also find that the optimal history length for each diatom closely matches the first inflection point of its velocity autocorrelation function, suggesting a link between model architecture and statistical mechanics. These results establish MAMD as a proof-of-concept integration strategy for the isolated harmonic diatomic systems studied here, in which finite velocity memory supports short-horizon predictions and sparse Hamiltonian check-ins provide long-horizon stability. In particular, we show that force-free, velocity-based machine learning updates can be embedded directly into conventional molecular dynamics algorithms while retaining essential physical invariants, providing a physically interpretable basis for hybrid MD/ML integration. Systematic extensions to more complex systems and quantitative performance comparisons in regimes with expensive force evaluations (e.g., ab initio molecular dynamics) are left for future work.

Partial decidability protocol for the Wang tiling problem from statistical mechanics and chaotic mapping

On the statistical physics and thermodynamics of polymer networks: An Eulerian theory for entropic elasticity

Ceramic balls, as an emerging grinding medium, require a systematic method for optimizing their size distribution in wet ball mills. This study proposes an innovative approach that integrates Duan’s semi-theoretical ball diameter formula with breakage statistical mechanics to determine the optimal ceramic ball size distribution. The ideal ball diameters for grinding 2.36–3.0 mm, 1.18–2.36 mm, 0.60–1.18 mm, and 0.30–0.60 mm tungsten ore were identified as 55 mm, 50 mm, 35 mm, and 20 mm, respectively. Subsequently, the optimal ball size distribution was formulated as CB3: Ø55 mm:Ø50 mm:Ø35 mm:Ø20 mm = 30%:40%:20%:10%. Comparative sieve analysis and discrete element method (DEM) simulations confirmed that the CB3 distribution yields the highest proportion of qualified particles, the most favorable collision frequency, and the greatest kinetic energy among all tested configurations. The proposed method demonstrates both accuracy and practicality, providing a theoretical foundation for the industrial application of ceramic ball grinding systems.

We consider an iterative branching process in which an abstract object can subdivide into other objects. The multiplication process may be varied by the occurrence of random "fatal" events in which some of the subsequent objects or states may fail. The process is also constrained to terminate upon reaching a given number of events or alternatively upon reaching a fixed number of iteration steps. A system of diophantine integer-variable equations capable of describing the aforementioned process is proposed. These equations can be applied prospectively to many branching phenomena of physical, biological and demographic nature. The equations, which we call systems of equations S, Q, U can be reformulated into three main classes based on the behavior of the sum of variables with respect to a fixed principal numerical parameter (TC= 'Total Cases'). These systems always admit solutions and these are sought for the three classes. The mathematical properties of the three systems are presented both analytically and graphically, and the software script for calculating numerical solutions is attached. In the case of high TC values, where direct calculation is not possible, special solutions are also sought for the steady state case and the "most probable" case, the latter using statistical mechanics methods. Solutions examples are given for a wide range of TC parameters. We also refer to real-world examples of applications ranging from prey/predator population dynamics to population mortality modeling and 2d lattice space tiling and also tree leaves branching alternatives. The main purpose of the study here proposed is to implement a mathematical frame that can provide tools to be used in the study of real-world applications.

Three body problem is one of the most complicated dynamical problems in classical mechanics; the difficulty comes from the nonlinear equations and sensitive initial conditions. In this paper, it reviews the disintegration process of Three body system in long-term evolution and discuss the application of statistical mechanics in explaining this phenomenon. Based on the theoretical model, numerical simulation, and observational results, it draws the following conclusions: The most frequent final state of a three-body system is the disintegration of a binary star and an escape star. This kind of mechanism comes from the energy and angular momentum’s homogenization, and it has been proved by the BN/KL region in Orion. Besides, the statistical model based on the microcanonical distribution and ergodicity assumption can predict the final state parameter’s distribution, which is consistent with the simulation results and provides a new way to explore chaotic systems. In the future, it will combine Gaia, gravitational wave observation, and high-precision numerical simulation to further complete the theory and application in the dynamics of compact objects.

Disordered biopolymer gels, such as alginate gels, contain disordered amorphous regions as well as ordered regions known as junction zones, the latter playing a paramount role in maintaining the integrity of the gel network. The considerable dimensions of these junction zones and their physical interactions are responsible for distinctive phenomena, such as self-healing, observed in biopolymer gels. Compared to rubber-like materials, where polymer chains are interconnected by chemical cross-links, statistical mechanics modeling of disordered biopolymer gels poses new challenges due to the need to capture the contributions from both the disordered and ordered regions. In the literature, the disordered domains are usually modeled by a collection of random coils, while each junction zone is represented by a rigid rod. Attempt has been made to introduce the two-node coil-rod structure, consisting of a random coil connected to a rigid rod, into classical polymer network models (e.g., the Arruda–Boyce eight-chain model) to predict the mechanical response of the biopolymer gels. Although this approach provides valuable insights and reasonable predictions that agree with experimental data, the interactions between the junction zones and the amorphous regions are significantly simplified. This study aims to extend the two-node coil-rod structure to a four-node coil-rod structure, in which two polymer chains share a junction zone, more explicitly representing chain association induced by physical forces in biopolymer gels. By incorporating statistical mechanics and the phantom network model, the entropy of the system is derived, from which the stress–stretch relationships for the network are obtained. Comparisons are made with the model based on the two-node coil-rod structure, and the conditions for establishing equivalency between the two methods are examined. This work establishes a foundation for developing more advanced network models that incorporates the simultaneous interaction of multiple junction zones, a phenomenon often present in biopolymer gels.

The current cosmological model, known as the \Lambda Λ -Cold Dark Matter model (or \Lambda Λ CDM for short) is one of the most astonishing accomplishments of contemporary theoretical physics. It is a well-defined mathematical model which depends on very few ingredients and parameters and is able to make a range of predictions and postdictions with astonishing accuracy. It is built out of well-known physics – general relativity, quantum mechanics and atomic physics, statistical mechanics and thermodynamics – and predicts the existence of new, unseen components. Again and again it has been shown to fit new data sets with remarkable precision. Despite these successes, we have yet to understand the unseen components of the Universe and there has been evidence for inconsistencies in the model. In these lectures, we lay the foundations of modern cosmology.

While quantum statistical mechanics triumphs in explaining many equilibrium phenomena, there is an increasing focus on going beyond conventional scenarios of thermalization. Traditionally examples of nonthermalizing systems are either integrable or disordered. Recently, examples of translationally invariant physical systems have been discovered whose excited energies avoid thermalization either due to local constraints (whether exact or emergent) or due to higher-form symmetries. In this article, we extend these investigations for the case of 3D U ( 1 ) quantum dimer models, which are lattice gauge theories with finite-dimensional local Hilbert spaces (also generically called quantum link models) with staggered charged static matter. Using a combination of analytical and numerical methods, we uncover a class of athermal states that arise in large winding sectors, when the system is subjected to external electric fields. The polarization of the dynamical fluxes in the direction of applied field traps excitations in 2D planes, while an interplay with the Gauss law constraint in the perpendicular direction causes exotic athermal behavior due to the emergence of new conserved quantities. This causes a geometric fragmentation of the system. We provide analytical arguments showing that the scaling of the number of fragments is exponential in the linear system size, leading to weak fragmentation. Further, we identify sectors which host fractonic excitations with severe mobility restrictions. The unitary evolution of fragments dominated by fractons is qualitatively different from the one dominated by nonfractonic excitations.

Abstract Local feature matching is a fundamental component of many computer vision tasks, including structure-from-motion, simultaneous localization and mapping, and visual localization. However, it remains challenging in low-texture regions and under extreme illumination variations. In this work, we present adaptive feature enhancement and statistical confidence modulation network (AFESCMNet), a lightweight network designed to improve feature robustness without compromising computational efficiency. AFESCMNet integrates two complementary modules: adaptive enhancement and statistical confidence modulation (SCM). The adaptive enhancement combines a dynamic dilated convolution modulator that adapts receptive fields based on local texture complexity, and feature importance learning that emphasizes discriminative channels. Although building upon known concepts, their specific integration and optimization for feature matching in challenging conditions represent the key contribution. The SCM introduces a statistical confidence fusion mechanism, which refines neural confidence predictions using low-level image statistics such as variance, gradient magnitude, and contrast, thereby improving keypoint reliability under textureless or illumination-varying conditions. Together, these components achieve a favorable balance between efficiency and robustness for lightweight feature matching. Built upon an optimized XFeat backbone with self-supervised regularization, AFESCMNet produces focused feature heatmaps and compact yet discriminative descriptors with minimal overhead. Extensive experiments on four benchmarks—relative pose estimation, homography estimation, visual localization, and 3D reconstruction—demonstrate that AFESCMNet consistently improves performance over representative lightweight baselines, achieving up to +3.3% higher accuracy in challenging nighttime localization scenarios, and preserving real-time performance on resource-constrained robotic platforms.