Nonequilibrium Dynamics Of Systems Research Articles

Nonequilibrium Schwinger-Keldysh formalism for density matrix states: Analytic properties and implications in cosmology

Motivated by cosmological Hartle-Hawking and microcanonical density matrix prescriptions for the quantum state of the Universe we develop a Schwinger-Keldysh in-in formalism for generic nonequilibrium dynamical systems with the initial density matrix. We build the generating functional of in-in Green’s functions and expectation values for a generic density matrix of the Gaussian type and show that the requirement of particle interpretation selects a distinguished set of positive/negative frequency basis functions of the wave operator of the theory, which is determined by the density matrix parameters. Then we consider a special case of the density matrix determined by the Euclidean path integral of the theory, which in the cosmological context can be considered as a generalization of the no-boundary pure state to the case of the microcanonical ensemble, and show that in view of a special reflection symmetry its Wightman Green’s functions satisfy Kubo-Martin-Schwinger periodicity conditions which hold despite the nonequilibrium and nonstationary nature of the physical setup. Rich analyticity structure in the complex plane of the time variable reveals the combined Euclidean-Lorentzian evolution of the theory, which depending on the properties of the initial density matrix can be interpreted as a decay of a classically forbidden quantum state. Published by the American Physical Society 2024

Attractors and bifurcation diagrams in complex climate models.

The climate is a complex nonequilibrium dynamical system that relaxes toward a steady state under the continuous input of solar radiation and dissipative mechanisms. The steady state is not necessarily unique. A useful tool to describe the possible steady states under different forcing is the bifurcation diagram, which reveals the regions of multistability, the position of tipping points, and the range of stability of each steady state. However, its construction is highly time consuming in climate models with a dynamical deep ocean, whose relaxation time is of the order of thousand years, or other feedback mechanisms that act on even longer time scales, like continental ice or carbon cycle. Using a coupled setup of the MIT general circulation model, we test two techniques for the construction of bifurcation diagrams with complementary advantages and reduced execution time. The first is based on the introduction of random fluctuations in the forcing and permits to explore a wide part of phase space. The second reconstructs the stable branches using estimates of the internal variability and of the surface energy imbalance on each attractor, and is more precise in finding the position of tipping points.

Toward implementing autonomous adaptive data acquisition for scanning hyperspectral imaging of biological systems

Autonomous experimentation is an emerging area of research, primarily related to autonomous vehicles, scientific combinatorial discovery approaches in materials science and drug discovery, and iterative research loops of planning, experimentation, and analysis. However, autonomous approaches developed in these contexts are difficult to apply to high-dimensional mapping technologies, such as scanning hyperspectral imaging of biological systems, due to sample complexity and heterogeneity. We briefly cover the history of adaptive sampling algorithms and surrogate modeling in order to define autonomous adaptive data acquisition as an objective-based, flexible building block for future biological imaging experimentation driven by intelligent infrastructure. We subsequently summarize the recent implementations of autonomous adaptive data acquisition (AADA) for scanning hyperspectral imaging, assess how these address the difficulties of autonomous approaches in hyperspectral imaging, and highlight the AADA design variation from a goal-oriented perspective. Finally, we present a modular AADA architecture that embeds AADA-driven flexible building blocks to address the challenge of time resolution for high-dimensional scanning hyperspectral imaging of nonequilibrium dynamical systems. In our example research-driven experimental design case, we propose an AADA infrastructure for time-resolved, noninvasive, and label-free scanning hyperspectral imaging of living biological systems. This AADA infrastructure can accurately target the correct state of the system for experimental workflows that utilize subsequent expensive, high-information-content analytical techniques.

Special Issue: Symmetry in Nonequilibrium Statistical Mechanics and Dynamical Systems

The recent developments in dynamical systems theory and non-equilibrium statistical mechanics have allowed the birth of new challenges and research perspectives. In particular, different frameworks have been proposed for the modeling of complex emerging phenomena occurring in nature and society. This editorial article introduces the topic and the contributions of this Special Issue. This Special Issue focuses, on the one hand, on the development of new methods, frameworks and models coming from dynamical system theory and the equilibrium/non-equilibrium statistical mechanics and, on the other hand, opens problems related to the existing frameworks. The Special Issue also includes applications to physical, biological and engineering systems.

The quasi-particle picture and its breakdown after local quenches: mutual information, negativity, and reflected entropy

We study the dynamics of (Rényi) mutual information, logarithmic negativity, and (Rényi) reflected entropy after exciting the ground state by a local operator. Together with recent results from ref. [1], we are able to conjecture a close-knit structure between the three quantities that emerges in states excited above the vacuum, including both local and global quantum quenches. This structure intimately depends on the chaoticity of the theory i.e. there exist distinct sets of equivalences for integrable and chaotic theories. For rational conformal field theories (RCFT), we find all quantities to compute the quantum dimension of the primary operator inserted. In contrast, we find the correlation measures to grow (logarithmically) without bound in all c > 1 conformal field theories with a finite twist gap. In comparing the calculations in the two classes of theories, we are able to identify the dynamical mechanism for the breakdown of the quasi-particle picture in 2D conformal field theories. Intriguingly, we also find preliminary evidence that our general lessons apply to quantum systems considerably distinct from conformal field theories, such as integrable and chaotic spin chains, suggesting a universality of entanglement dynamics in non-equilibrium systems.

Multiscale structural complexity of natural patterns

Complexity of patterns is key information for human brain to differ objects of about the same size and shape. Like other innate human senses, the complexity perception cannot be easily quantified. We propose a transparent and universal machine method for estimating structural (effective) complexity of two-dimensional and three-dimensional patterns that can be straightforwardly generalized onto other classes of objects. It is based on multistep renormalization of the pattern of interest and computing the overlap between neighboring renormalized layers. This way, we can define a single number characterizing the structural complexity of an object. We apply this definition to quantify complexity of various magnetic patterns and demonstrate that not only does it reflect the intuitive feeling of what is "complex" and what is "simple" but also, can be used to accurately detect different phase transitions and gain information about dynamics of nonequilibrium systems. When employed for that, the proposed scheme is much simpler and numerically cheaper than the standard methods based on computing correlation functions or using machine learning techniques.

Geochemistry landscape classification: toxicity of chemical elements and their impact on human health

In the article, the following were considered: classification of geochemical landscapes of the investigated territory, migration and accumulation of toxic chemical elements and their impact on human health. The research article was carried out in two directions: the first part-migration patterns of the chemical elements. The migration of chemical elements by landscape types has been identified, and a map has been developed showing the migration of chemical elements across the landscape. The second part of the article explores the toxicity of chemical elements that are common in the area and examines the relationship between the diseases observed in areas where the toxic elements are most commonly encountered and their effects on human health. The article is devoted to the study of the peculiarities of the geochemical transformation of landscapes in the research area (of the Kura intermountain basin) based on the patterns of concentration and migration of macro-compounds and trace elements found in samples of mountain rocks, soil, plants and water, for which a comparative method of research and the relationship of landscape components was used. For the first time, a medium-scale "Geochemical classification of landscapes" and then "map scheme of diseases caused by anomalous concentration of microelements" of this region were compiled. The article reveals the characteristic features of the compiled maps and the features of the geochemical transformation of the study area. The geochemistry of landscapes studies the patterns of migration of chemical elements in the Earth's geographical shell. It deals with patterns of substance migration in that shell of the Earth that is the place of human life. The landscape is a fundamental concept of natural science as "chemical element," mineral, "soil." The landscape is a large and complex nonequilibrium dynamic system of the Earth's surface, in which the elements of the lithohydrology and atmosphere are interpenetrated.

Dissipation Function: Nonequilibrium Physics and Dynamical Systems.

An exact response theory has recently been developed within the field of Nonequilibrium Molecular Dynamics. Its main ingredient is known as the Dissipation Function, . This quantity determines nonequilbrium properties like thermodynamic potentials do with equilibrium states. In particular, can be used to determine the exact response of particle systems obeying classical mechanical laws, subjected to perturbations of arbitrary size. Under certain conditions, it can also be used to express the response of a single system, in contrast to the standard response theory, which concerns ensembles of identical systems. The dimensions of are those of a rate, hence can be associated with the entropy production rate, provided local thermodynamic equilibrium holds. When this is not the case for a particle system, or generic dynamical systems are considered, can equally be defined, and it yields formal, thermodynamic-like, relations. While such relations may have no physical content, they may still constitute interesting characterizations of the relevant dynamics. Moreover, such a formal approach turns physically relevant, because it allows a deeper analysis of and of response theory than possible in case of fully fledged physical models. Here, we investigate the relation between linear and exact response, pointing out conditions for the validity of the response theory, as well as difficulties and opportunities for the physical interpretation of certain formal results.

First-principles molecular dynamics investigation of ceria/silica sliding interface toward functional materials design for chemical mechanical polishing process

We report a form of chemical mechanical polishing (CMP) in which ceria abrasive particles polish a silicon wafer surface in a water environment. The Car-Parrinello molecular dynamics (CPMD) method, which enables chemical reaction dynamics in non-equilibrium systems to be treated non-empirically, was used. The first application of CPMD was to a model including a silica surface rubbed by a ceria cluster to ascertain the fundamental tribochemical phenomena in the CMP process. The model consisted of a hydrogen-terminated silica surface (a representative model of an oxidized wafer surface) and H4Ce6O12 cluster placed in the vicinity of an asperity in the silica surface. H2O molecules were explicitly considered in order to reflect the presence of slurry water. An external load and shear force were applied to the cluster. Under conditions of finite temperature and friction, a Ce-O-Si bridging bond formed at the interface between the silica surface and the ceria cluster. Subsequently, another Ce-O-Si bridging bond formed. These newly formed bridging bonds changed the silicon atom into a five-coordinated one. Because this state was probably unstable, a pyramid structure was rapidly restored by breaking the original Si-O bond in the asperity, meaning that the wafer surface became flattened. By referring to static density functional theory (DFT) calculations, we concluded that this bond dissociation event was due to multiple Ce-O-Si bonds forming. To discuss the effect of slurry water, a similar CPMD simulation, but without H2O molecules (i.e., dry friction), was performed. Here, the Si-O bond dissociation reaction did not take place even if multiple Ce-O-Si bonds formed. This means slurry water is needed for CMP to occur and it probably helps to weaken the Si-O bond. The second application of CPMD was to a model consisting of a thin water layer sandwiched between silica and ceria plates for studying the effect of the surface orientation of the ceria. Two low-index CeO2 surfaces, (100) and (111), were modeled. A chemical event wherein Ce-O-Si bridging bonds formed on the ceria/silica interface could be observed in both models. However, the bond dissociation reaction of the original Si-O bond on the silica surface proceeded only in the model with the (111) surface, and not on the (100) surface. This difference in reactivity could mainly be explained by the arrangement of atoms of each surface. The (111) surface provides hexagonal adsorption sites that inherently form a structure with five-coordinated silicon atoms, which are important intermediates in the CMP process. On the other hand, the (100) surface exhibits square adsorption sites which hardly form the required intermediate. We successfully examined the effect of the surface orientation of the ceria in addition to the fundamental CMP mechanism wherein multiple Ce-O-Si bonds initiate a chemical reaction including Si-O bond scission.

Type-II quadrupole topological insulators

Modern theory of electric polarization is formulated by the Berry phase, which, when quantized, leads to topological phases of matter. Such a formulation has recently been extended to higher electric multipole moments, through the discovery of the so-called quadupole topological insulator. It has been established by a classical electromagnetic theory that in a two-dimensional material the quantized properties for the quadupole topological insulator should satisfy a basic relation. Here we discover a new type of quadrupole topological insulator (dubbed type-II) that violates this relation due to the breakdown of the correspondence that a Wannier band and an edge energy spectrum close their gaps simultaneously. We find that, similar to the previously discovered (referred to as type-I) quadrupole topological insulator, the type-II hosts topologically protected corner states carrying fractional corner charges. However, the edge polarizations only occur at a pair of boundaries in the type-II insulating phase, leading to the violation of the classical constraint. We demonstrate that such new topological phenomena can appear from quench dynamics in non-equilibrium systems, which can be experimentally observed in ultracold atomic gases. We also propose an experimental scheme with electric circuits to realize such a new topological phase of matter. The existence of the new topological insulating phase means that new multipole topological insulators with distinct properties can exist in broader contexts beyond classical constraints.

Steady-state distributions and nonsteady dynamics in nonequilibrium systems.

We search for steady states in a class of fluctuating and driven physical systems that exhibit sustained currents. We find that the physical concept of a steady state, well known for systems at equilibrium, must be generalized to describe such systems. In these, the generalization of a steady state is associated with a stationary probability density of microstates and a deterministic dynamical system whose trajectories the system follows on average. These trajectories are a manifestation of nonstationary macroscopic currents observed in these systems. We determine precise conditions for the steady state to exist as well as the requirements for it to be stable. We illustrate this with some examples.

Predicting Nonequilibrium Patterns beyond Thermodynamic Concepts: Application to Radiation-Induced Microstructures

In this work, we derive an analytical model to predict the appearance of all possible radiation-induced steady states and their associated microstructures in immiscible A_{c[over ¯]}B_{1-c[over ¯]} alloys, an example of a nonequilibrium dynamical system. This model is assessed against numerical simulations and experimental results which show that different microstructures characterized by the patterning of A-rich precipitates can emerge under irradiation. We demonstrate that the steady-state microstructure is governed by irradiation conditions and also by the average initial concentration of the alloy c[over ¯]. Such a dependence offers new leverage for tailoring materials with specific microstructures overcoming limitations imposed by the equilibrium thermodynamic phase diagram.

Unequal time correlators of stochastic scalar fields in de Sitter space

The quantum fluctuations of a test scalar field on superhorizon scale in de Sitter spacetime can be described by an effective one-dimensional stochastic theory corresponding to a particular class of nonequilibrium dynamical systems known as the model A. Using the formulation of the latter in terms of a supersymmetric field theory, we compute various unequal-time correlators at large (superhorizon) time separations and compare with existing quantum field theory computation. This includes perturbative calculations, pushed here up to three-loop order, and a nonperturbative $1/N$ expansion at next-to-leading order. Exploiting the supersymmetry of the stochastic theory, we also derive a spectral representation of the field correlators and a fluctuation-dissipation relation for the infrared modes of the scalar field in de Sitter spacetime.

Quantifying the flux as the driving force for nonequilibrium dynamics and thermodynamics in non-Michaelis–Menten enzyme kinetics

The driving force for active physical and biological systems is determined by both the underlying landscape and nonequilibrium curl flux. While landscape can be experimentally quantified from the histograms of the collected real-time trajectories of the observables, quantifying the experimental flux remains challenging. In this work, we studied the single-molecule enzyme dynamics of horseradish peroxidase with dihydrorhodamine 123 and hydrogen peroxide (H2O2) as substrates. Surprisingly, significant deviations in the kinetics from the conventional Michaelis-Menten reaction rate were observed. Instead of a linear relationship between the inverse of the enzyme kinetic rate and the inverse of substrate concentration, a nonlinear relationship between the two emerged. We identified nonequilibrium flux as the origin of such non-Michaelis-Menten enzyme rate behavior. Furthermore, we quantified the nonequilibrium flux from experimentally obtained fluorescence correlation spectroscopy data and showed this flux to led to the deviations from the Michaelis-Menten kinetics. We also identified and quantified the nonequilibrium thermodynamic driving forces as the chemical potential and entropy production for such non-Michaelis-Menten kinetics. Moreover, through isothermal titration calorimetry measurements, we identified and quantified the origin of both nonequilibrium dynamic and thermodynamic driving forces as the heat absorbed (energy input) into the enzyme reaction system. Furthermore, we showed that the nonequilibrium driving forces led to time irreversibility through the difference between the forward and backward directions in time and high-order correlations were associated with the deviations from Michaelis-Menten kinetics. This study provided a general framework for experimentally quantifying the dynamic and thermodynamic driving forces for nonequilibrium systems.

Microscopic dynamics, chaos and transport in nonequilibrium processes

This EPJ - Special Topics issue is a collection of contributions on theory and the recent developments in nonequilibrium statistical mechanics, fluctuations theory and dynamical systems. The various articles report results on the role of microscopic dynamics in giving rise to complex patterns observed at the macroscopic scale in a variety of physical phenomena.

Deterministic Irreversibility and The Matter Structure

The role of existence of the deterministic irreversibility mechanism in development of evolution physics is studied. The short explanation of physical essence of this mechanism is offered. Based on this mechanism, is proved, that the base element of matter should be an open non-equilibrium dynamic system (ONDS). The principles of the emergence, existence and development of the ONDS hierarchical structure are considered. The questions about hierarchy of the matter and existence of stationary states ONDS are studied. The question, how external constraints determine of the evolution of ONDS, is analyzed. Equations that determine the development of ONDS are submitted.

Closed hierarchies and non-equilibrium steady states of driven systems

We present a class of tractable non-equilibrium dynamical quantum systems which includes combinations of injection, detection and extraction of particles interspersed by unitary evolution. We show how such operations generate a hierarchy of equations tying lower correlation functions with higher order ones. The hierarchy closes for particular choices of measurements and leads to a rich class of evolutions whose long time behavior can be simulated efficiently. In particular, we use the method to describe the dynamics of current generation through a generalized quantum exclusion process, and exhibit an explicit formula for the long time energy distribution in the limit of weak driving.

Determinism in Physics and Cognoscibility of a Picture of the World

The purpose of the article is to show the key role of the deterministic mechanism of irreversibility (DMI) in the understanding of the picture of the world and in its construction. For this, a brief analysis of the historical development of the picture of the world and the tasks of its further development, connected with the problems of describing the processes of evolution in the framework of the laws of fundamental physics, has been carried out. It is shown how DMI removes these problems. The role of DMI in the statement of the principle of causality in physics is studied. It is shown how DMI contributes to the realization of the ideas of universal evolutionism. It also shows how the conclusion that the open non-equilibrium dynamic system should be an element of matter and why matter should be a hierarchy of such systems follows from the condition of DMI existence. Using the example of the relationship between the laws of the evolution of systems and the laws of the dynamics of their elements, it is demonstrated how the law of transition of quantity to quality is implemented in physics and how one can build a picture of the world from simplicity to complexity. It is shown how with the help of numerical methods possible to substantiate that the laws of thermodynamics, statistical physics follow from the fundamental laws of nature.

Optimal Data-Driven Estimation of Generalized Markov State Models for Non-Equilibrium Dynamics

There are multiple ways in which a stochastic system can be out of statistical equilibrium. It might be subject to time-varying forcing; or be in a transient phase on its way towards equilibrium; it might even be in equilibrium without us noticing it, due to insufficient observations; and it even might be a system failing to admit an equilibrium distribution at all. We review some of the approaches that model the effective statistical behavior of equilibrium and non-equilibrium dynamical systems, and show that both cases can be considered under the unified framework of optimal low-rank approximation of so-called transfer operators. Particular attention is given to the connection between these methods, Markov state models, and the concept of metastability, further to the estimation of such reduced order models from finite simulation data. All these topics bear an important role in, e.g., molecular dynamics, where Markov state models are often and successfully utilized, and which is the main motivating application in this paper. We illustrate our considerations by numerical examples.

Non-extensive statistical analysis on solar activity dependence of magnetospheric dynamics

Tsallis q-Gaussian distributions and associated q-statistics have been used for the last couple of decades to describe non-equilibrium dynamical systems with varying degrees of complexity. In the present study, we use Tsallis non-extensive statistical analysis for a better understanding of magnetospheric dynamics and its relationship with solar activity. The Tsallis' q-triplet, a set of indices (such as qsens, qstat and qrel) used as empirical quantifiers of non-extensivity, has been estimated for magnetospheric proxies such as auroral electrojet (AE) and disturbance storm time (Dst) indices, for a period of 1985–2007. Our results indicate that the degree of non-extensivity of AE index is quite different from that of Dst index in relation with solar activity dependence. We have seen that the values of the q-triplets calculated from Dst index are more solar activity dependent than those computed from AE index. This shows that, other than solar wind exertions, certain complex phenomena of internal origin also modulate the dynamics of geomagnetic fluctuations in the auroral region.