Statistical Physics Research Articles

An Econophysics Perspective on Green Bonds and Stock Market Nexus: Can Green Finance be an Investment Option for Emerging Stock Markets?

Green bonds are one of the most fascinating financial innovations that offer a solution to climate change and sustainable development from the financial point of view. In this study, we employ methods from statistical physics to examine the multifractal features of cross-correlations between green bonds and emerging stock markets. Utilizing multifractal detrended cross-correlation analysis (MFDCCA) on return and volatility series, our findings reveal significant cross-correlations between green bonds and emerging stock markets. The MFDCCA results uncover multifractal features and long-range cross-correlations between the two assets. Notably, volatility cross-correlations exhibit persistent behavior, while return cross-correlations vary across small and large fluctuation periods. These findings hold practical implications for policymakers and investors involved in green bonds and emerging stock markets.

Pair correlations of logarithms of complex lattice points

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Non-Hermitian non-equipartition theory for trapped particles

The equipartition theorem is an elegant cornerstone theory of thermal and statistical physics. However, it fails to address some contemporary problems, such as those associated with optical and acoustic trapping, due to the non-Hermitian nature of the external wave-induced force. We use stochastic calculus to solve the Langevin equation and thereby analytically generalize the equipartition theorem to a theory that we denote the non-Hermitian non-equipartition theory. We use the non-Hermitian non-equipartition theory to calculate the relevant statistics, which reveal that the averaged kinetic and potential energies are no longer equal to kBT/2 and are not equipartitioned. As examples, we apply non-Hermitian non-equipartition theory to derive the connection between the non-Hermitian trapping force and particle statistics, whereby measurement of the latter can determine the former. Furthermore, we apply a non-Hermitian force to convert a saddle potential into a stable potential, leading to a different type of stable state.

Thermal Conductivity of a Fluid-Filled Nanoporous Material: Underlying Molecular Mechanisms and the Rattle Effect.

Nanoporous materials are central to the energy and environmental crisis, with key applications in adsorption, separation, and catalysis. While confinement and surface effects on fluids severely confined in their porosity are well documented, the thermal behavior of nanoporous solids subjected to fluid adsorption remains puzzling in many aspects. With striking phenomena such as the so-called rattle effect, through which fluid/solid collisions decrease the overall thermal conductivity, the solid thermal conductivity and, more generally, heat transfer and dispersion in these complex systems challenge classical approaches (e.g., mixing rules including effective medium approaches fail to capture such effects as shown here). In particular, a robust molecular framework to describe the crossover between the decrease in thermal conductivity through the rattle effect in very narrow pores and the increase in thermal conductivity when replacing vacuum with a fluid phase in larger pores is still missing. Here, using a prototypical model of fluid-filled nanoporous materials (a Lennard-Jones phase confined in an all-silica zeolite), we perform a molecular simulation study to shed light on the parameters that govern the rattle effect in nanoporous solids. First, by varying the fluid/fluid, fluid/solid, and solid/solid interaction strengths as well as the fluid number density and mass density, we unravel the ingredients that lead to the essential coupling between fluid adsorption and phonon transport. Second, despite this complex interplay, inspired by pioneering molecular approaches on the rattle effect, we show that all data obey a simple statistical physics model that relies on the change in the speed of sound due to the fluid adsorbed density and the decrease in phonon lifetime due to scattering by fluid molecules. This framework, which provides a simple formalism to rationalize the thermal behavior of this class of solid/fluid composites, points to a decrease in thermal conductivity upon fluid confinement (up to 30% in some cases). Such an effect paves the way for the design of novel applications involving fluids in interaction with nanoporous materials.

Assessment and modeling of mercury adsorption on carbon-based adsorbents prepared from Jacaranda mimosifolia and guava biomass via pyrolysis and hydrothermal carbonization

Abstract The mercury adsorption properties of carbon-based materials prepared from jacaranda (Jacaranda mimosifolia) and guava (Psidium guajava) seed wastes are reported and compared in this paper. These adsorbent samples were obtained via pyrolysis and hydrothermal carbonization. Mercury adsorption equilibrium was studied at pH 4 and 20–40 °C, and the adsorption enthalpy changes were calculated for all adsorbent samples. The results showed that jacaranda-based materials contained a higher amount of acidic functional groups than guava seed-based adsorbents, and consequently, their mercury adsorption properties were better. The surface area of these adsorbents was <10 m2/g thus being classified as low-porosity materials. Elemental analysis indicated that all adsorbents were mainly composed of oxygen (4–25%) and carbon (75–95%). The calculated adsorption capacities at saturation of the best adsorbent were 18.05–30.09 mg/g under the tested experimental conditions. Statistical physics calculations also indicated that the adsorption mechanism of HgCl2 species was multi-molecular and endothermic. Ligand exchange and van der Waals forces were involved in generating the mercury–adsorbent interface. These results highlight the importance of comparing and optimizing biomass thermochemical conversion routes to tailor the surface properties of adsorbents used for water purification.

Phosphorus recovery from urine by CO2-activated biochar for sustainable slow-release fertilizer applications: Unveiling adsorption mechanisms by statistical physics modeling and predictive modeling with artificial neural networks

The global phosphorus crisis necessitates efficient phosphorus recovery, crucial for sustainable practices. This study introduces CAMLB, a CO2-activated Magnolia grandiflora leaf-based biochar, as an effective adsorbent for phosphorus capture from artificial urine and subsequently served as a sustainable slow-release fertilizer. Adsorbent characterization results implied the involvement of electrostatic attraction, ligand exchange, ion exchange, pore filling, hydrogen bonding, and surface precipitation in the adsorption process. Statistical physical outcomes reveals that the physical adsorption process is characterized by multi-ion adsorption, an inclined orientation, and an endothermic, reversible nature. Artificial neural network (ANN) models validate adsorption kinetics and isotherm data with high precision (R > 0.99). Additionally, spent biochar proves valuable as a slow-release fertilizer, promoting wheat germination and growth. Overall, this paper offers a circular economy approach for achieving the recycling of urine wastewater and agricultural waste and focuses on unraveling the mechanisms of phosphorus recovery.

A novel magnetic geopolymer-based adsorbent prepared from heated glauconite and separated magnetite: Experiments and statistical physics treatment for crystal violet

Sinai copper ore with 9.48 % of Fe2O3 was treated using a laboratory-scale mineral processing techniques that included size reduction (below 75 µm) and a wet low intensity drum-type magnetic separation. After this treatment method, the separated magnetite product containing about 85 % of Fe2O3 was extracted. A mixture of heated glauconite (900 °C/2h) and the extracted magnetite was activated by sodium silicate (Na2SiO3) to obtain a novel glauconite-based magnetic geopolymer (namely GMG). Several analytical techniques (i.e., XRD, XRF, FESEM, FTIR, EDX, TEM, elemental mapping, and zeta potential) were used in the characterization of GMG and its performance for crystal violet (CRV) remediation was studied. The equilibrium data at pH 8.0 and 25 – 50 °C were fitted to a statistical physics multilayer model and classical isotherm equations to understand the CRV adsorption mechanism. The theoretical calculations indicated that GMG can adsorb 1.12 to 1.39 of CRV molecules per functional group (n), suggesting the presence of a multi-interaction mechanism and vertical adsorption orientation on GMG surface. For this basic dye, the estimated saturation adsorption capacities (Qsat) ranged from 684 to 612 mg/g, and an exothermic binding interaction was associated with the removal of this dye molecule. The adsorption energies (ΔE) ranged between 15.05 and 36.74 kJ/mol, indicating that physical forces, such as electrostatic interactions and hydrogen bonds, governed the GMG-CRV interactions. After fourth adsorption–desorption cycles, the regenerated GMG showed 74 % of its adsorption capacities, which suggested the suitability of this adsorbent to be regenerated and reused multiple times in water treatment. Overall, the combination between the separated magnetite and glauconite was an effective approach for the remediation of effluents that contain dye molecules

Moments of undersampled distributions: Application to the size of epidemics

The total number of fatalities of an epidemic outbreak is a dramatic but extremely informative quantity. Knowledge of the statistics of this quantity allows the calculation of the mean total number of fatalities conditioned to the fact that the outbreak has surpassed a given number of fatalities, which is very relevant for risk assessment. However, the fact that the total number of fatalities seems to be characterized by a power-law tailed distribution with exponent (for the complementary cumulative distribution function) smaller than one poses an important theoretical difficulty, due to the non-existence of a mean value for such distributions. Cirillo and Taleb (2020) propose a transformation from a so-called dual variable, which displays a power-law tail, to the total number of fatalities, which becomes bounded by the total world population. Here, we (i) show that such a transformation is ad hoc and unphysical; (ii) propose alternative transformations and distributions (also ad hoc); (iii) argue that the right framework for this problem is statistical physics, through finite-size scaling; and (iv) demonstrate that the real problem is not the non-existence of the mean value for power-law tailed distributions but the fact that the tail of the different theoretical distributions (which is what distinguishes one model from the other) is far from being well sampled with the available number of empirical data. Our results are also valid for many other hazards displaying (apparent) power-law tails in their size.

Detection of financial bubbles using a log‐periodic power law singularity (LPPLS) model

AbstractThis article provides a systematic review of the theoretical and empirical academic literature on the development and extension of the log‐periodic power law singularity (LPPLS) model, which is also known as the Johansen–Ledoit–Sornette (JLS) model or log‐periodic power law (LPPL) model. Developed at the interface of financial economics, behavioral finance and statistical physics, the LPPLS model provides a flexible and quantitative framework for detecting financial bubbles and crashes by capturing two salient empirical characteristics of price trajectories in speculative bubble regimes: the faster‐than‐exponential growth of price leading to unsustainable growth ending with a finite crash‐time and the accelerating log‐periodic oscillations. We also demonstrate the LPPLS model by detecting the recent bubble status of the S&P 500 index between April 2020 and December 2022, during which the S&P 500 index reaches its all‐time peak at the end of 2021. We find that the strong corrections of the S&P 500 index starting from January 2022 stem from the increasingly systemic instability of the stock market itself, while the well‐known external shocks, such as the decades‐high inflation, aggressive monetary policy tightening by the Federal Reserve, and the impact of the Russia/Ukraine war, may serve as sparks.This article is categorized under: Applications of Computational Statistics > Computational Finance Algorithms and Computational Methods > Computational Complexity Statistical Models > Nonlinear Models

Complex systems in ecology: a guided tour with large Lotka–Volterra models and random matrices

Ecosystems represent archetypal complex dynamical systems, often modelled by coupled differential equations of the form d x i d t = x i ϕ i ( x 1 , … , x N ) , where N represents the number of species and x i , the abundance of species i . Among these families of coupled differential equations, Lotka–Volterra (LV) equations, corresponding to ϕ i ( x 1 , … , x N ) = r i − x i + ( Γ x ) i , play a privileged role, as the LV model represents an acceptable trade-off between complexity and tractability. Here, r i is the intrinsic growth of species i and Γ stands for the interaction matrix: Γ i j represents the effect of species j over species i . For large N , estimating matrix Γ is often an overwhelming task and an alternative is to draw Γ at random, parameterizing its statistical distribution by a limited number of model features. Dealing with large random matrices, we naturally rely on random matrix theory (RMT). The aim of this review article is to present an overview of the work at the junction of theoretical ecology and large RMT. It is intended to an interdisciplinary audience spanning theoretical ecology, complex systems, statistical physics and mathematical biology.

Selective Extraction and Determination of Hydrocortisone and Dexamethasone in Skincare Cosmetics: Analytical Interpretation Using Statistical Physics Formalism

Molecularly imprinted polymers (MIPs), as magnetic extraction adsorbents, are used for the selective, rapid determination and extraction of dexamethasone and hydrocortisone in skincare products. Therefore, in this paper, magnetic molecularly imprinted polymers (MMIPs) and magnetic non-molecularly imprinted polymers (MNIPs) were utilized as adsorbents to describe the adsorption phenomena of dexamethasone and hydrocortisone. This interpretation, based on a statistical physics theory, applies the multilayer model with saturation to comprehend the adsorption of the drugs. Results obtained via numerical simulation revealed that dexamethasone and hydrocortisone adsorption happens via a non-parallel orientation on the surfaces of MMIPs and MNIPs, and they also showed that the adsorption amount of the MMIPs for the template molecule was notably greater than that of the MNIPs at the same initial concentration. The adsorption energy values retrieved from the data analysis ranged between 7.65 and 15.77 kJ/mol, indicating that the extraction and determination of dexamethasone and hydrocortisone is a physisorption process. Moreover, the distribution of a site’s energy was calculated to confirm the physical nature of the interactions between adsorbate/adsorbent and the heterogeneity of the surfaces of the MMIPs and MNIPs. Finally, the thermodynamic interpretation confirmed the exothermicity and spontaneous nature of the adsorption of these drugs on the tested adsorbents.

Dynamic nonreversibility view of intrinsic brain organization and brain dynamic analysis of repetitive transcranial magnitude stimulation.

Intrinsic neural activities are characterized as endless spontaneous fluctuation over multiple time scales. However, how the intrinsic brain organization changes over time under local perturbation remains an open question. By means of statistical physics, we proposed an approach to capture whole-brain dynamics based on estimating time-varying nonreversibility and k-means clustering of dynamic varying nonreversibility patterns. We first used synthetic fMRI to investigate the effects of window parameters on the temporal variability of varying nonreversibility. Second, using real test-retest fMRI data, we examined the reproducibility, reliability, biological, and physiological correlation of the varying nonreversibility substates. Finally, using repetitive transcranial magnetic stimulation-fMRI data, we investigated the modulation effects of repetitive transcranial magnetic stimulation on varying nonreversibility substate dynamics. The results show that: (i) as window length increased, the varying nonreversibility variance decreased, while the sliding step almost did not alter it; (ii) the global high varying nonreversibility states and low varying nonreversibility states were reproducible across multiple datasets and different window lengths; and (iii) there were increased low varying nonreversibility states and decreased high varying nonreversibility states when the left frontal lobe was stimulated, but not the occipital lobe. Taken together, these results provide a thermodynamic equilibrium perspective of intrinsic brain organization and reorganization under local perturbation.

Opinion Models, Election Data, and Political Theory.

A unifying setup for opinion models originating in statistical physics and stochastic opinion dynamics are developed and used to analyze election data. The results are interpreted in the light of political theory. We investigate the connection between Potts (Curie-Weiss) models and stochastic opinion models in the view of the Boltzmann distribution and stochastic Glauber dynamics. We particularly find that the q-voter model can be considered as a natural extension of the Zealot model, which is adapted by Lagrangian parameters. We also discuss weak and strong effects (also called extensive and nonextensive) continuum limits for the models. The results are used to compare the Curie-Weiss model, two q-voter models (weak and strong effects), and a reinforcement model (weak effects) in explaining electoral outcomes in four western democracies (United States, Great Britain, France, and Germany). We find that particularly the weak effects models are able to fit the data (Kolmogorov-Smirnov test) where the weak effects reinforcement model performs best (AIC). Additionally, we show how the institutional structure shapes the process of opinion formation. By focusing on the dynamics of opinion formation preceding the act of voting, the models discussed in this paper give insights both into the empirical explanation of elections as such, as well as important aspects of the theory of democracy. Therefore, this paper shows the usefulness of an interdisciplinary approach in studying real world political outcomes by using mathematical models.

The Use of Computer Mathematics Systems for Solving Some Problems of Thermodynamics and Statistical Physics

With the help of the MathCAD mathematical package, solutions to problems using the heat balance equation were obtained, in which the heat capacity was calculated according to Debye theory, and spline interpolation of experimental data on heat capacity from the reference book was also used. The degree of helium ionization at a given temperature is calculated. An example of the influence of lithium impurity on the degree of hydrogen ionization is considered. The energy and pressure of neon in the region of multiple ionization are calculated. Isotherms of an ideal fermi gas are con structed. A graph of the Fermi-Dirac distribution function for various temperatures is constructed. The concentration of electrons and positrons at temperatures corresponding to the rest energy of electrons is calculated. These examples can be used in the educational process.

Solution to the schrödinger equation for bound states of polar molecules using shallow neural networks

The time independent Schrödinger equation can be solved analytically in very few cases. This is why scientists rely on approximate numerical methods. One that is yet to be a part of the everyday toolbox for physicists are neural networks. With it, it is possible to calculate eigenfunctions and the energy spectra of bound states. A double exponential central potential is used to describe the interaction between two electric dipoles that form through van der Waals interactions. These systems can be important when the electric dipoles are very large and differ from covalent, ionic, and other kinds of bonds, as is the case of the monomers M−C60, where M=Cs,Li or other alkali metals. Based in statistical physics, it has been shown that a dimer can be formed through a spontaneous and exothermic reaction. The ground state and the first two excited states of this system were calculated, also the solutions and their associated energies were plotted. The result for the ground state is compared to the shooting method and the direct variational method. The numerical value of the ground states obtained suggests that the dimers can be dissociated by electromagnetic waves with wavelengths in the far infrared regime, very close to microwaves.

Effectiveness of educational interventions in minimizing reactance in traffic accident prevention

IntroductionClassical mechanics concepts are vital for understanding traffic safety, encompassing speed, acceleration, stopping distance, impact speed, deformation, kinetic energy, and their effects on vehicle occupants. Statistical physics principles are also employed to study multiple vehicles as a many-particle system. This study examines the effectiveness of using a damaged car and structured instruction in road safety initiatives.MethodsParticipants engaged with a damaged car and discussed deformation caused by excessive speed. They participated in role simulations, envisioning and solving risky traffic scenarios, while considering the potential boomerang effect resulting from excessive fear appeals within the campaign.ResultsCombining emotional appeals with solution-focused, action-oriented, and self-esteem-enhancing interventions is essential to mitigate the boomerang effect and encourage safety-compliant behavior. Educational institutions must implement tailored follow-ups to emotionally charged prevention campaigns. Using Design-Based Research, we developed effective methods for knowledge acquisition and transfer, drawing from cognitive behavioral therapy and established traffic safety programs.DiscussionThis publication explores non-standardized social training within focus groups, focusing on negative emotional states following an emotionalizing campaign similar to “Crash Kurs NRW,” targeting upper-level courses in North Rhine-Westphalian schools. Methods from cognitive behavioral therapy and social learning initiated, observed, and documented changes in participants’ norms, values, and attitudes, discussed herein. Additionally, we investigated whether the presence of police officers in prevention campaigns influences reactive behavior. Comparing pre- and post-surveys confirmed reactance after emotionalizing campaigns, and our structured post-survey effectively influenced stage-event-induced behavior. Surprisingly, police officers’ presence did not significantly impact reactive behavior. Furthermore, our follow-up tool extends its applicability to similar emotionalizing prevention campaigns, broadening its potential reach. Our future research will delve into students’ physics literacy during traffic space analysis of accident hotspots, advancing traffic safety initiatives.

Neodymium adsorption from aqueous solution by β-cyclodextrin nanosponges and a polymer valorized from potato peels waste: experiments and conventional and statistical physics interpretations.

Using organic waste and residue streams to be turned into valuable and greener materials for various applications has proven an efficient and suitable strategy. In this work, two green materials (nanosponges and a polymer) were synthesized using potato peels and applied for the first time to adsorb and recover Neodymium (Nd3+) from aqueous solutions. The recovery of Nd3+ that belongs to the rare earth elements has attracted important interest due to its/their importance in several industrial and technological applications. The fine potato peel waste (FPPW) polymer presented an irregular shape and porous surface. At the same time, the β-cyclodextrin (β-CD) nanosponges had uniform distribution with regular and smooth shapes. β-CD nanosponges exhibited a much higher total carboxyl content (4.02mmolg-1) than FPPW (2.50mmolg-1), which could impact the Nd3+ adsorption performance because carboxyl groups can interact with cations. The adsorption capacity increased with the increase of the pH, reaching its maximum at pHs 6-7 for β-CD nanosponges and 4-7 for FPPW polymer. The kinetic and equilibrium data were well-fitted by General order and Liu models. β-CD nanosponges attained adsorption capacity near 100mg Nd per gram of adsorbent. Thermodynamic and statistical physical results corroborated that the adsorption mechanism was due to electrostatic interaction/complexation and that the carboxyl groups were important in the interactions. β-CD nanosponges (three cycles of use) were more effective than FPPW (one cycle of use) in the regeneration. Finally, β-CD nanosponges could be considered an eco-friendly adsorbent to recover Nd3+ from aqueous matrices.

A hybrid forecasting framework based on MCS and machine learning for higher dimensional and unbalanced systems

Forecasting methods and theories have been widely researched and applied in complex systems and fields such as statistical physics, econophysics, material crystals, etc. However, challenges persist in applying these methods to complex systems characterized by high dimensionality, data imbalance, and single prediction evaluation. To address these issues, we propose a novel hybrid forecasting approach that integrates the model confidence set (MCS) with machine learning (ML) models. We introduce Principal Component Analysis (PCA) to reduce dimensionality of the data, reduce data imbalance through a combination of random undersampling and oversampling, and introduce several metrics to evaluate the machine learning model set. We also introduce the MCS to select the optimal model from the set of ML models and propose a new combinatorial approach, the MCS-ML combinatorial model. An empirical study is conducted using the example of abnormal transactions in the Bitcoin blockchain. The empirical results show that the proposed MCS-ML combinatorial model has better predictive performance than the models in the ML model set under different data structures.

Multifractal Detrended Cross-Correlations between Green Bonds and Commodity Markets: An Exploration of the Complex Connections between Green Finance and Commodities from the Econophysics Perspective

Green bonds represent a compelling financial innovation that presents a financial perspective solution to address climate change and promote sustainable development. On the other hand, the recent process of financialisation of commodities disrupts the dynamics of the commodity market, increasing its correlation with financial markets and raising the risks associated with commodities. In this context, understanding the dynamics of the interconnectivity between green bonds and commodity markets is crucial for risk management and portfolio diversification. This study aims to reveal the multifractal cross-correlations between green bonds and commodities by employing methods from statistical physics. We apply multifractal detrended cross-correlation analysis (MFDCCA) to both return and volatility series, demonstrating that green bonds and commodities exhibit multifractal characteristics. The analysis reveals long-range power-law cross-correlations between these two markets. Specifically, volatility cross-correlations persist across various fluctuations, while return series display persistence in small fluctuations and antipersistence in large fluctuations. These findings carry significant practical implications for hedging and risk diversification purposes.

Homophily modulates double descent generalization in graph convolution networks

Graph neural networks (GNNs) excel in modeling relational data such as biological, social, and transportation networks, but the underpinnings of their success are not well understood. Traditional complexity measures from statistical learning theory fail to account for observed phenomena like the double descent or the impact of relational semantics on generalization error. Motivated by experimental observations of "transductive" double descent in key networks and datasets, we use analytical tools from statistical physics and random matrix theory to precisely characterize generalization in simple graph convolution networks on the contextual stochastic block model. Our results illuminate the nuances of learning on homophilic versus heterophilic data and predict double descent whose existence in GNNs has been questioned by recent work. We show how risk is shaped by the interplay between the graph noise, feature noise, and the number of training labels. Our findings apply beyond stylized models, capturing qualitative trends in real-world GNNs and datasets. As a case in point, we use our analytic insights to improve performance of state-of-the-art graph convolution networks on heterophilic datasets.