Nonadditive Systems Research Articles

Machine learning assisted phase and size-controlled synthesis of iron oxide particles

Synthesis of iron oxides with specific phases and particle sizes is a crucial challenge in various fields, including materials science, energy storage, biomedical applications, environmental science, and earth science. However, despite significant advances in this area, much of the current palette of particle outcomes has been based on time-consuming trial-and-error exploration of synthesis conditions. The present study was designed to explore a very different approach to 1) predict the outcome of synthesis from specified reaction parameters based on using machine learning (ML) techniques, and 2) correlate sets of parameters to obtain products with desired outcomes by a newly designed recommendation algorithm. To achieve this, four ML algorithms were tested, namely random forest, logistic regression, support vector machine, and k-nearest neighbor. Among the models, random forest outperformed the others, attaining 96% and 81% accuracy when predicting the phase and size of iron oxide particles in the test dataset. Surprisingly, the permutation feature importance analysis revealed that volume, which may strongly relate to pressure, was one of the important features, along with precursor concentration, pH, temperature, and time, influencing the phase and size of iron oxide particles during synthesis. To verify the robustness of the random forest models, prediction and experimental results were compared based on 24 randomly generated methods in additive and non-additive systems not included in the datasets. The predictions of product phase and particle size from the models agreed well with the experimental results. Furthermore, a searching and ranking algorithm was developed to recommend potential synthesis parameters for obtaining iron oxide products with the desired phase and particle size from previous studies in the dataset. This study lays the foundation for a closed-loop approach in materials synthesis and preparation, beginning with suggesting potential reaction parameters from the dataset and predicting potential outcomes, followed by conducting experiments and analyses, and ultimately enriching the dataset.

Entanglement propagation and dynamics in non-additive quantum systems

The prominent collective character of long-range interacting quantum systems makes them promising candidates for quantum technological applications. Yet, lack of additivity overthrows the traditional picture for entanglement scaling and transport, due to the breakdown of the common mechanism based on excitations propagation and confinement. Here, we describe the dynamics of the entanglement entropy in many-body quantum systems with a diverging contribution to the internal energy from the long-range two body potential. While in the strict thermodynamic limit entanglement dynamics is shown to be suppressed, a rich mosaic of novel scaling regimes is observed at intermediate system sizes, due to the possibility to trigger multiple resonant modes in the global dynamics. Quantitative predictions on the shape and timescales of entanglement propagation are made, paving the way to the observation of these phases in current quantum simulators. This picture is connected and contrasted with the case of local many body systems subject to Floquet driving.

From the Boltzmann equation with non-local correlations to a standard non-linear Fokker-Planck equation

In this work, we study the formal connections between the non-linear Fokker-Planck Equation associated with the non-additive entropy and the Boltzmann Equation with the non-additive correlation functional. The collisional term following the q-algebra is adopted. In the derivation of the non-additive Fokker-Planck Equation, two constraints are imposed on the final result: i) that the entropic index q is a characteristic parameter of the non-additive systems with a value that does not change with time, and ii) that for q→1 a smooth transition for the standard Fokker-Planck Equation is obtained.

Artificial neural network states for nonadditive systems

Methods inspired from machine learning have recently attracted great interest in the computational study of quantum many-particle systems. So far, however, it has proven challenging to deal with microscopic models in which the total number of particles is not conserved. To address this issue, we propose a variant of neural network states, which we term neural coherent states. Taking the Fr\"ohlich impurity model as a case study, we show that neural coherent states can learn the ground state of nonadditive systems very well. In particular, we recover exact diagonalization in all regimes tested and observe substantial improvement over the standard coherent state estimates in the most challenging intermediate-coupling regime. Our approach is generic and does not assume specific details of the system, suggesting wide applications.

Microcanonical Characterization of First-Order Phase Transitions in a Generalized Model for Aggregation

Aggregation transitions in disordered mesoscopic systems play an important role in several areas of knowledge, from materials science to biology. The lack of a thermodynamic limit in systems that are intrinsically finite makes the microcanonical thermostatistics analysis, which is based on the microcanonical entropy, a suitable alternative to study the aggregation phenomena. Although microcanonical entropies have been used in the characterization of first-order phase transitions in many non-additive systems, most of the studies are only done numerically with aid of advanced Monte Carlo simulations. Here we consider a semi-analytical approach to characterize aggregation transitions that occur in a generalized model related to the model introduced by Thirring. By considering an effective interaction energy between the particles in the aggregate, our approach allowed us to obtain scaling relations not only for the microcanonical entropies and temperatures, but also for the sizes of the aggregates and free-energy profiles. In addition, we test the approach commonly used in simulations which is based on the conformational microcanonical entropy determined from a density of states that is a function of the potential energy only. Besides the evaluation of temperature versus concentration phase diagrams, we explore this generalized model to illustrate how one can use the microcanonical thermostatistics as an analysis method to determine experimentally relevant quantities such as latent heats and free-energy barriers of aggregation transitions.

РАЗВИТИЕ ПОНЯТИЯ ОБ ЭНТРОПИИ: ОТ ТЕРМОДИНАМИКИ ДО КОСМОЛОГИИ. СООБЩЕНИЕ 2. ГИПОТЕЗА ОБ ЭНТРОПИИ В КОСМОЛОГИИ И ЕЕ РАЗВИТИЕ

In the work [7], the classical concepts of thermodynamic entropy are systematized and modern approaches to assessing the tribo-fatigue and mechanothermodynamic entropy of non-additive systems are outlined. In this article, the concept of the analogy of thermodynamics and mechanics of black holes is presented and analyzed, which made it possible to estimate their (thermodynamic) entropy. The insufficiency of this concept is that thermodynamic entropy is a characteristic of energy dissipation, whereas black holes are characterized by the absorption of energy and matter. In this regard, it is proposed to consider the event horizon as a hermodynamic medium, and a black hole as a tribo-fatigue object. And then the “black hole — event horizon” system is presented as a combined mechanothermodynamic non-additive multisystem. Methods for estimating the total (mechanothermodynamic) entropy and its components — tribo-fatigue and thermodynamic entropy in black hole mechanics are presented. With regard to individual (specific) zones and objects of the universe, the well-known theory of Zeldovich is accordingly modified: the universe is a thermodynamic medium with discretely distributed (scattered) dense and/or solid bodies (objects) — stars, galaxies, etc. Behavior of such a system (direct and back effects in the universe) are described. The peculiarity of the action of the medium on the stars and, conversely, the action of the cluster of stars on the interaction between them consists in the fact that it is non-Newtonian: action is not equal to reaction. It is the inequality of action against counteraction, which has radically different mechanisms and consequences (results), or, in other words, the imbalance of the universe that determine its general motion in space–time. The changing set of all states is the evolution of the universe. The analysis of possible strategies for the evolution of mechanothermodynamic systems is carried out on the basis of the fundamental principle: the damageability of everything that exists has no conceivable boundaries. This principle is formulated in mechanothermodynamics and used in philosophy to create a generalized theory of the evolution of the material world.

Characterization of the non-Arrhenius behavior of supercooled liquids by modeling nonadditive stochastic systems.

The characterization of the formation mechanisms of amorphous solids is a large avenue for research, since understanding its non-Arrhenius behavior is challenging to overcome. In this context, we present one path toward modeling the diffusive processes in supercooled liquids near glass transition through a class of nonhomogeneous continuity equations, providing a consistent theoretical basis for the physical interpretation of its non-Arrhenius behavior. More precisely, we obtain the generalized drag and diffusion coefficients that allow us to model a wide range of non-Arrhenius processes. This provides a reliable measurement of the degree of fragility of the system and an estimation of the fragile-to-strong transition in glass-forming liquids, as well as a generalized Stokes-Einstein equation, leading to a better understanding of the classical and quantum effects on the dynamics of nonadditive stochastic systems.

Evolutionary Innovations and Where to Find Them: Routes to Open-Ended Evolution in Natural and Artificial Systems

This article presents a high-level conceptual framework to help orient the discussion and implementation of open-endedness in evolutionary systems. Drawing upon earlier work by Banzhaf et al. (2016), three different kinds of open-endedness are identified: exploratory, expansive, and transformational. These are characterized in terms of their relationship to the search space of phenotypic behaviors. A formalism is introduced to describe three key processes required for an evolutionary process: the generation of a phenotype from a genetic description, the evaluation of that phenotype, and the reproduction with variation of individuals according to their evaluation. The formalism makes explicit various influences in each of these processes that can easily be overlooked. The distinction is made between intrinsic and extrinsic implementations of these processes. A discussion then investigates how various interactions between these processes, and their modes of implementation, can lead to open-endedness. However, an important contribution of the article is the demonstration that these considerations relate to exploratory open-endedness only. Conditions for the implementation of the more interesting kinds of open-endedness-expansive and transformational-are also discussed, emphasizing factors such as multiple domains of behavior, transdomain bridges, and non-additive compositional systems. In contrast to a traditional Darwinian analysis, these factors relate not to the generic evolutionary properties of individuals and populations, but rather to the nature of the building blocks out of which individual organisms are constructed, and the laws and properties of the environment in which they exist. The article ends with suggestions of how the framework can be used to categorize and compare the open-ended evolutionary potential of different systems, how it might guide the design of systems with greater capacity for open-ended evolution, and how it might be further improved.

Concavity, Response Functions and Replica Energy.

In nonadditive systems, like small systems or like long-range interacting systems even in the thermodynamic limit, ensemble inequivalence can be related to the occurrence of negative response functions, this in turn being connected with anomalous concavity properties of the thermodynamic potentials associated with the various ensembles. We show how the type and number of negative response functions depend on which of the quantities E, V and N (energy, volume and number of particles) are constrained in the ensemble. In particular, we consider the unconstrained ensemble in which E, V and N fluctuate, which is physically meaningful only for nonadditive systems. In fact, its partition function is associated with the replica energy, a thermodynamic function that identically vanishes when additivity holds, but that contains relevant information in nonadditive systems.

An examination of the nature and dynamics of seismogenesis in South California, USA, based on Non-Extensive Statistical Physics

We examine the nature of the seismogenetic system in South California, USA, by searching for evidence of complexity and non-extensivity in the earthquake record. We attempt to determine whether earthquakes are generated by a self-excited Poisson process, in which case they are independent, or by a Critical process, in which long-range interactions in non-equilibrium states are expected (correlation). Emphasis is given to background seismicity, i.e. to the rudimentary expression of the seismogenetic system. We use the complete and homogeneous earthquake catalogue published by the South California Earthquake Data Centre, in which aftershocks are either included, or have been removed by a stochastic declustering procedure. We examine multivariate cumulative frequency distributions of earthquake magnitudes, interevent time and interevent distance in the context of Non-Extensive Statistical Physics, which generalizes the additive Boltzmann-Gibbs thermodynamics to non-additive (non-extensive) dynamic systems. Our results indicate that the seismogenetic systems of South California are generally sub-extensive complex and certainly non-Poissonian. Background seismicity exhibits long-range interaction as evidenced by the overall increase of correlation observed by declustering the earthquake catalogues, as well as by the high correlation observed for earthquakes separated by long interevent distances. The results compare very well with those obtained in previous work for the seismogenetic systems of North California. Specifically, the Walker Lane – Eastern California Shear Zone on one hand, and the San Andreas Fault system – south California Continental Borderland region on the other, appear to comprise fault networks with different dynamics and expression. The former exhibits persistent, very high correlation and has attributes of (stationary) Self-Organized Criticality (SOC). The latter exhibits high correlation mainly at long ranges and has attributes of evolutionary of (Self-Organized) Criticality. All in all, our results are compatible with simulations of small-world fault networks in which free boundary conditions at the surface allow for self-organization and criticality to develop.

Nonadditivity of nanoparticle interactions.

Understanding interactions between inorganic nanoparticles (NPs) is central to comprehension of self-organization processes and a wide spectrum of physical, chemical, and biological phenomena. However, quantitative description of the interparticle forces is complicated by many obstacles that are not present, or not as severe, for microsize particles (μPs). Here we analyze the sources of these difficulties and chart a course for future research. Such difficulties can be traced to the increased importance of discreteness and fluctuations around NPs (relative to μPs) and to multiscale collective effects. Although these problems can be partially overcome by modifying classical theories for colloidal interactions, such an approach fails to manage the nonadditivity of electrostatic, van der Waals, hydrophobic, and other interactions at the nanoscale. Several heuristic rules identified here can be helpful for discriminating between additive and nonadditive nanoscale systems. Further work on NP interactions would benefit from embracing NPs as strongly correlated reconfigurable systems with diverse physical elements and multiscale coupling processes, which will require new experimental and theoretical tools. Meanwhile, the similarity between the size of medium constituents and NPs makes atomic simulations of their interactions increasingly practical. Evolving experimental tools can stimulate improvement of existing force fields. New scientific opportunities for a better understanding of the electronic origin of classical interactions are converging at the scale of NPs.

Thermodynamics of Nonadditive Systems.

The usual formulation of thermodynamics is based on the additivity of macroscopic systems. However, there are numerous examples of macroscopic systems that are not additive, due to the long-range character of the interaction among the constituents. We present here an approach in which nonadditive systems can be described within a purely thermodynamics formalism. The basic concept is to consider a large ensemble of replicas of the system where the standard formulation of thermodynamics can be naturally applied and the properties of a single system can be consequently inferred. After presenting the approach, we show its implementation in systems where the interaction decays as 1/r(α) in the interparticle distance r, with α smaller than the embedding dimension d, and in the Thirring model for gravitational systems.

A statistical manifold modeled on Orlicz spaces using Kaniadakis κ-exponential models

Given a probability measure μ, on the space of strictly positive densities Mμ, we construct a topological manifold on which the elements are connected by κ-exponential models in the form q=expκ⁡(u⊖κKp,κ(u))p, where expκ⁡(x)=(1+κ2x2+κx)1/κ, x⊖κy=x1+κ2y2−y1+κ2x2, p,q∈Mμ, and their local representations are elements of an Orlicz space, i.e. the manifold is modeled on Orlicz spaces. Parameter k is the G. Kaniadakis parameter for κ-deformed exponentials which is strongly relevant to relativity and statistical complex models in statistical mechanics. Functional Kp,κ is the deformed counterpart of the cumulant mapping and satisfies that, if κ→0, we obtain the usual cumulant functional of the exponential manifold; moreover in this limit case the exponential manifold constructed by Pistone and Sempi is recovered. In the context of deformed exponentials, we prove that the function ϕκ(⋅)=coshκ⁡(⋅)−1, where coshκ⁡(x) is the κ-deformed hyperbolic cosine, is a Young function and generates the Orlicz space on which the κ-exponential manifold is modeled, namely Lϕκ(p⋅μ). This construction differs from the one made by Pistone on the paper κ-exponential models from the geometrical viewpoint, since this last one is based on divergence functionals and modeled on Lebesgue spaces L1/κ(p⋅μ). The use of κ-deformed models is interesting since they generalize the exponential models and extend them to non-additive systems.

Non-additivity in laser-illuminated many-atom systems.

We show that atoms subject to laser radiation may form a non-additive many-body system on account of their long-range forces, when the atoms are trapped in the vicinity of a fiber with a Bragg grating. When the laser frequency is inside the grating's bandgap but very close to its edge, we find that the range and strength of the laser-induced interaction becomes substantially enhanced, due to the large density of states near the edge, while the competing process of scattering to the fiber is inhibited. The dynamics of the atomic positions in this system conforms to a prominent model of statistical physics which exhibits slow relaxation. This suggests the possibility of using laser-illuminated atoms to study the characteristics of non-additive systems.

Modified quantum-behaved particle swarm optimization for parameters estimation of generalized nonlinear multi-regressions model based on Choquet integral with outliers

In this paper, a generalized nonlinear multi-regression model based on Choquet integral (NMRCI) is proposed and applied for estimation of non-additive systems that include outliers under inherent i...

Modified quantum-behaved particle swarm optimization for parameters estimation of generalized nonlinear multi-regressions model based on Choquet integral with outliers

In this paper, a generalized nonlinear multi-regression model based on Choquet integral (NMRCI) is proposed and applied for estimation of non-additive systems that include outliers under inherent interaction among inputs. The parameters estimation for the proposed model is also performed via a modified algorithm based on particle swarm optimization with quantum-behavior (QPSO), named MQPSO. From the proposed model, the high breakdown regression estimator, a least trimmed squares (LTS) is applied to eliminate the influence caused by these observations that contain outliers. Besides, elitist crossover of genetic algorithm (GA) and adaptive decay of simulated annealing (SA) are used for conquering premature and controlling search policy, respectively. Hence, the proposed MQPSO algorithm which combines the mechanisms of GA, SA and LTS within the QPSO algorithm can deal with the proposed model with outliers. From simulation results, the proposed MQPSO readily corrects the deviation caused by outliers without losing precisions and swiftly achieves convergences on estimating the parameters of the proposed generalized NMRCI model for the non-additive systems with outliers.

Control Functions and Simultaneous Equations Methods

The control function approach is a convenient method of estimation in simultaneous equation systems. This requires that the system can be expressed in triangular form with variables satisfying a conditional mean independence restriction. Linear simultaneous models with additive errors can always be expressed in this form. However, in nonlinear nonadditive simultaneous systems, conditional independence requires a strong additional restriction known as control function separability. We argue that nonadditive models are a key characteristic of simultaneous models of economic behavior with unobserved heterogeneity. We review alternative “system” approaches and document the biases that occur when the control function approach is used inappropriately.

Genetic variability, correlation, path analysis and construction of selection index in mulberry silkworm, <i>Bombyx mori</i> L. I. Genetic variability

The genotypic variability and heritability for nine quantitative characters in 65 varieties of silkworm, B. mori L. have been investigated. Variation among genotypes were highly significant (p<0.001) for all the characters indicating the existence of a real difference among the genotypes which are suitable for breeding purposes. The highest heritability was obtained for shell weight followed by filament size (FS), filament length (FL), expected cocoon yield out of 100 dfls (ECY), surviving percentage of larvae (SPL), cocoon weight (CW), egg hatching percentage (EHP) and mature larval weight (MLW). Comparatively high heritability accompanied by a genetic advance was recorded for FL and total number of eggs laid per female (TEL) indicating the importance of additive gene effects of these characters, but shell weight, cocoon weight and filament size showed high heritability and low genetic advance indicating the involvement of non-additive gene systems in the inheritance of these characters. So selection on the basis of these characters, with relatively more emphasis upon filament length and total number of eggs laid per female to obtain high yielding varieties of B. mori is suggested. DOI: http://dx.doi.org/10.3329/ujzru.v30i0.10744 Univ. j. zool. Rajshahi Univ. Vol. 30, 2011 pp.33-36

Termodinâmica do modelo de Ising com interações de alcance infinito via ensemble canônico generalizado

Apresentamos nesse trabalho a ideia de como ensembles generalizados podem ser utilizados para simplificar operacionalmente o estudo de sistemas físicos não aditivos. Como alternativa aos métodos tradicionais de integração direta ou teoria de campo médio, mostramos como a solução do modelo de Ising com interações de alcance infinito é obtida utilizando um ensemble canônico generalizado. Descrevemos como as propriedades termodinâmicas para esse modelo na presença de um campo magnético externo são encontradas por meio de simples equações paramétricas. Sem prejuízos a interpretação usual, obtemos um comportamento crítico identico ao observado nas abordagens tradicionais.

Phase equilibria in polydisperse nonadditive hard-sphere systems

Colloidal particles naturally exhibit a size polydispersity that can greatly influence their phase behavior in solution. Nonadditive hard-sphere (NAHS) mixtures are simple and well-suited model systems to represent phase transitions in colloid systems. Here, we propose an analytical equation of state (EOS) for NAHS fluid mixtures, which can be straightforwardly applied to polydisperse systems. For positive values of the nonadditivity parameter Delta the model gives accurate predictions of the simulated fluid-fluid coexistence curves and compressibility factors. NPT Monte Carlo simulations of the mixing properties of the NAHS symmetric binary mixture with Delta>0 are reported. It is shown that the enthalpy of mixing is largely positive and overcomes the positive entropy of mixing when the pressure is increased, leading to a fluid-fluid phase transition with a lower critical solution pressure. Phase equilibria in polydisperse systems are predicted with the model by using the density moment formalism [P. Sollich, Adv. Chem. Phys. 116, 265 (2001)]. We present predictions of the cloud and shadow curves for polydisperse NAHS systems composed of monodisperse spheres and polydisperse colloid particles. A fixed nonadditivity parameter Delta > 0 is assumed between the monodisperse and polydisperse spheres, and a Schulz distribution is used to represent the size polydispersity. Polydispersity is found to increase the extent of the immiscibility region. The predicted cloud and shadow curves depend dramatically on the upper cutoff diameter sigmac of the Schulz distribution, and three-phase equilibria can occur for large values of sigmac.