Nonequilibrium Dissipative Systems Research Articles

Emergence of energy-avoiding and energy-seeking behaviors in nonequilibrium dissipative quantum systems

A longstanding challenge in nonequilibrium thermodynamics is to predict the emergence of self-organized behaviors and functionalities typical of living matter. Despite the progress with classical complex systems, it remains far from obvious how to extrapolate these results down to the quantum scale. Here, we employ the paradigmatic master equation framework to establish that some lifelike behaviors and functionalities can indeed emerge in elementary dissipative quantum systems driven out of equilibrium. Specifically, we find both energy-avoiding (low steady dissipation) and energy-seeking behaviors (high steady dissipation), as well as self-adaptive shifts between these modes, in generic few-level systems. We also find emergent functionalities, namely, a self-organized thermal gradient in the system’s environment (in the energy-seeking mode) and an active equilibration against thermal gradients (in the energy-avoiding mode). Finally, we discuss the possibility that our results could be related to the concept of dissipative adaptation.

Mesoscopic Pitting Oscillation-Induced Periodic Anodic Layer Electrodissolution of Au(111).

The electrodissolution of Au(111) in anaerobic cupric/ammonia/thiosulfate solutions, typical of a non-equilibrium dissipative system, was investigated via in situ electrochemical atomic force microscopy. At a specific initial concentration ratio of aqueous ammonia to cupric ions, the pit number and average pit area increase autocatalytically, while the pit depth increases monotonically during dissolution. A further increase in this initial concentration ratio leads to oscillatory dynamics in the pit number and average pit area while the pit depth fluctuates between one and two atoms. Mechanistic analysis indicates that alternation between formation and dissolution of a sulfur film results in periodic pitting, which produces gold dissolution layer by layer. This work presents a new dissolution mode, i.e., periodic layer dissolution generated by oscillatory pitting processes in addition to a pitting mode with a continually increasing depth, and the use of high initial concentration ratios of ammonia to cupric ion to accelerate the elimination of passivating sulfur film for Au dissolution.

Turbulence-Induced Rogue Waves in Kerr Resonators

Spontaneous emergence of self-organized patterns and their bifurcations towards a regime of complex dynamics in nonequilibrium dissipative systems is a paradigm of phase transition. Indeed, the behavior of these patterns in the highly nonlinear regime remains less explored, even in recent high-quality-factor resonators such as Kerr-nonlinear optical ones. Here, we investigate theoretically and experimentally the alteration of the resulting Kerr frequency combs from the weakly to the highly nonlinear regime, in the frameworks of spatiotemporal chaos, and dissipative phase transitions. We reveal the existence of a striking and easily accessible scenario of spatiotemporal chaos, free of cavity solitons, in a monostable operating regime, wherein a transition to amplitude turbulence via spatiotemporal intermittency is evidenced. Moreover, statistics of the light bursts in the resulting turbulent regime unveils the existence of rogue waves as extreme events characterized by long-tail statistics.6 MoreReceived 25 July 2018Revised 19 December 2018DOI:https://doi.org/10.1103/PhysRevX.9.011054Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBifurcationsPattern formationSpatiotemporal chaosNonlinear DynamicsGeneral Physics

Intelligent system for statistically significant expertise knowledge on the basis of the model of self-organizing nonequilibrium dissipative system

Development of the modern educational technologies caused by broad introduction of comput-er testing and development of distant forms of education does necessary revision of methods of an examination of pupils. In work it was shown, need transition to mathematical criteria, exami-nations of knowledge which are deprived of subjectivity. In article the review of the problems arising at realization of this task and are offered approaches for its decision. The greatest atten-tion is paid to discussion of a problem of objective transformation of rated estimates of the ex-pert on to the scale estimates of the student. In general, the discussion this question is was con-cluded that the solution to this problem lies in the creation of specialized intellectual systems. The basis for constructing intelligent system laid the mathematical model of self-organizing nonequilibrium dissipative system, which is a group of students. This article assumes that the dissipative system is provided by the constant influx of new test items of the expert and non-equilibrium – individual psychological characteristics of students in the group. As a result, the system must self-organize themselves into stable patterns. This patern will allow for, relying on large amounts of data, get a statistically significant assessment of student. To justify the pro-posed approach in the work presents the data of the statistical analysis of the results of testing a large sample of students (> 90). Conclusions from this statistical analysis allowed to develop intelligent system statistically significant examination of student performance. It is based on data clustering algorithm (k-mean) for the three key parameters. It is shown that this approach allows you to create of the dynamics and objective expertise evaluation.

Self-Organization and Semiosis in Jazz Improvisation

The complex systems principle of self-organization provides a new way of understanding the behavioral dynamics behind the emergent, spontaneous exchanges of musical performance. In biological self-organization, energy is expended in the form of work which operates to maintain order in a system, collectively constraining the possible behaviors the components of the system can exhibit. When two self-organized systems become closely coupled they form a synergistic, teleodynamic system, such that in a circularly causal manner each system's work helps to maintain and self-sustain one another's behavioral dynamics. The semiotic exchange between two improvising jazz musicians can also be understood as forming a synergistic, teleodynamic system, with musicians expending energy in the form of musical ‘work' that operates to mutually constrain the semiotic form of their own and their co-musicians playing behavior. In more specific terms, the two musicians form a higher-order autopoietic system that both creates and maintains the collective order of the co-playing musicians via the nonlinear, self-organizing dynamics that characterize non-equilibrium dissipative systems. Here the authors introduce this self-organization framework and describe its implications for developing new theories of musical semiotics that adequately address the spontaneous and emergent nature of improvised musical performances. The authors also describe how corresponding methods of non-linear time series analyses can provide the tools necessary for explicating the dynamical processes that shape such complex social exchanges.

Dissipative structures of quantized vortices in a coherently pumped polariton superfluid

Steady states reached in a coherently pumped exciton-polariton superfluid are investigated. As the pump parameter is changed, the translational symmetry of the uniform system is spontaneously broken, and various steady patterns of quantized vortices are formed. This is peculiar to nonequilibrium dissipative systems with continuous pumping.

How Physicists Made Stable Lévy Processes Physically Plausible

Stable Levy processes have very interesting properties for describing the complex behaviour of non-equilibrium dissipative systems such as turbulence, anomalous diffusion or financial markets. However, although these processes better fit the empirical data, some of their statistical properties can raise several theoretical problems in empirical applications because they generate infinite variables. Econophysicists have developed statistical solutions to make these processes physically plausible. This paper presents a review of these analytical solutions (truncations) for stable Levy processes and how econophysicists transformed them into data-driven processes. The evolution of these analytical solutions is presented as a progressive research programme provided by (econo)physicists for theoretical problems encountered in financial economics in the 1960s and the 1970s.

Multiscale Magnetic Underdense Regions on the Solar Surface: Granular and Mesogranular Scales

The Sun is a non-equilibrium dissipative system subjected to an energy flow which originates in its core. Convective overshooting motions create temperature and velocity structures which show a temporal and spatial evolution. As a result, photospheric structures are generally considered to be the direct manifestation of convective plasma motions. The plasma flows on the photosphere govern the motion of single magnetic elements. These elements are arranged in typical patterns which are observed as a variety of multiscale magnetic patterns. High resolution magnetograms of quiet solar surface revealed the presence of magnetic underdense regions in the solar photosphere, commonly called voids, which may be considered a signature of the underlying convective structure. The analysis of such patterns paves the way for the investigation of all turbulent convective scales from granular to global. In order to address the question of magnetic structures driven by turbulent convection at granular and mesogranular scales we used a "voids" detection method. The computed voids distribution shows an exponential behavior at scales between 2 and 10 Mm and the absence of features at 5-10 Mm mesogranular scales. The absence of preferred scales of organization in the 2-10 Mm range supports the multiscale nature of flows on the solar surface and the absence of a mesogranular convective scale.

Modulational instability and exact solutions of nonlinear cubic complex Ginzburg-Landau equation of thermodynamically open and dissipative warm ion acoustic waves system

Using the standard reductive perturbation technique, a nonlinear cubic complex Ginzburg-Landau equation (CGL3) is derived to study the modulational instability of ion acoustic waves (IAWs) in an unmagnetized plasma consisting of warm adiabatic ions and non-thermal electrons, which form the background. The CGL3 is exactly solved by using two methods: the separation of variables and the complex tanh function which produces four solutions; the results are compared and good agreement exists in most predictions. The CGL3 admits localized envelope (solitary wave) solutions of bright and dark types. We study the effects of the thermal conductivity of ions and non-thermally distributed electrons $ \beta$ on the modulational stability. The effect of ion thermal conductivity makes the frequency $ \omega$ be complex in the nonlinear dispersion relation. In terms of the first mode $ \omega_{{1}}^{}$ , the amplitude of the wave moving in the (+ ve) x -direction decreases when any one of the parameters $ \beta$ and the temperature ratio $ \sigma$ (= T i/T eff) increases (where Teff and Ti are the effective and ion temperatures, respectively). It is found that the whole k - $ \sigma$ plane transforms to an unstable region as $ \beta$ $ \approx$ 0.85 . Referring to the internal energy formula, the order of magnitude ratios of different kinds and contributions of the internal energy changes are calculated for various sets { $ \sigma$ , $ \beta$ } . The obtained results encourage us to name the unstable system --which experiences loss and gain of ions escaping out or embedding themselves into the acoustic frequency domain, collision and recently experimentally due to ionization and deionization-- a non-equilibrium thermodynamic dissipative open IAW system.

A statistical mechanical approach for the computation of the climatic response to general forcings

Abstract. The climate belongs to the class of non-equilibrium forced and dissipative systems, for which most results of quasi-equilibrium statistical mechanics, including the fluctuation-dissipation theorem, do not apply. In this paper we show for the first time how the Ruelle linear response theory, developed for studying rigorously the impact of perturbations on general observables of non-equilibrium statistical mechanical systems, can be applied with great success to analyze the climatic response to general forcings. The crucial value of the Ruelle theory lies in the fact that it allows to compute the response of the system in terms of expectation values of explicit and computable functions of the phase space averaged over the invariant measure of the unperturbed state. We choose as test bed a classical version of the Lorenz 96 model, which, in spite of its simplicity, has a well-recognized prototypical value as it is a spatially extended one-dimensional model and presents the basic ingredients, such as dissipation, advection and the presence of an external forcing, of the actual atmosphere. We recapitulate the main aspects of the general response theory and propose some new general results. We then analyze the frequency dependence of the response of both local and global observables to perturbations having localized as well as global spatial patterns. We derive analytically several properties of the corresponding susceptibilities, such as asymptotic behavior, validity of Kramers-Kronig relations, and sum rules, whose main ingredient is the causality principle. We show that all the coefficients of the leading asymptotic expansions as well as the integral constraints can be written as linear function of parameters that describe the unperturbed properties of the system, such as its average energy. Some newly obtained empirical closure equations for such parameters allow to define such properties as an explicit function of the unperturbed forcing parameter alone for a general class of chaotic Lorenz 96 models. We then verify the theoretical predictions from the outputs of the simulations up to a high degree of precision. The theory is used to explain differences in the response of local and global observables, to define the intensive properties of the system, which do not depend on the spatial resolution of the Lorenz 96 model, and to generalize the concept of climate sensitivity to all time scales. We also show how to reconstruct the linear Green function, which maps perturbations of general time patterns into changes in the expectation value of the considered observable for finite as well as infinite time. Finally, we propose a simple yet general methodology to study general Climate Change problems on virtually any time scale by resorting to only well selected simulations, and by taking full advantage of ensemble methods. The specific case of globally averaged surface temperature response to a general pattern of change of the CO2 concentration is discussed. We believe that the proposed approach may constitute a mathematically rigorous and practically very effective way to approach the problem of climate sensitivity, climate prediction, and climate change from a radically new perspective.

Competition of Self-Organized Rotating Helical Autowaves in Nonequilibrium Dissipative System with Three-Level Active Centers

Competition of self-organized rotating helical autowaves is computationally studied in a nonequilibrium dissipative system possessing the excitability and the two-channel diffusion of excitations. This system consists of three-level active centers interacting locally properties of which are close to the properties of active centers in a phaser (a microwave phonon laser). Dynamical stabilization and coexistence of rotating helical autowaves with different topological charges have been observed under conditions of their weak competition. A self-induced sign reversal phenomenon of a topological charge has been revealed in the case of strongly competing rotating helical autowaves; the mechanism of this nonlinear phenomenon is found. Prospects of investigations of rotating helical autowaves in nonequilibrium dissipative systems with excitable three-level active canters are discussed.

S-matrix description of nonequilibrium finite-temperature systems

We consider the “inclusive” (“partial”) method for describing nonequilibrium dissipative systems at the early (kinetic) evolution stage, when the temperature distribution is nonuniform. We formulate the perturbation theory in terms of space-time-local temperature Green’s functions and derive the Liouville equation for the one-particle partition function.

Self-organization of surface wave sustained discharges in the pressure range from 10 to 200 Torr

Experiments showing the dynamics in the self-organization of surface wave sustained discharges are presented. Microwave (2.4 GHz) discharges maintained in an argon gas in a continuous wave regime at a constant applied power and varying gas pressure are studied. The evolution of the discharge from a stationary plasma column at comparatively low pressure (p⩽10 Torr) to a plasma torch at atmospheric pressure passes through different stages of self-organization of the wave-field↔plasma nonlinear structure showing evidence of the general trends of behavior of nonequilibrium dissipative systems. The measurements are carried out at the stage of the discharge self-organization into a filamentary structure with an azimuthal rotation. Macroscopic characteristics (number, size, velocity of rotation) of the filaments and their dependence on the gas pressure and its time variation are given. The total light emission of the plasma considered as giving information about the plasma density is measured and different methods of signal processing (including correlation-spectrum analysis) are applied. Oscillations of the filament ends are also observed. The different types of interrelation between plasma density and field intensity, registrated in the different pressure ranges, call for variety in the instability mechanisms. Although the scenario of the discharge self-organization is stressed in the discussions, the observations are important with their relation to the discharge applications, which require avoiding conditions of development of instabilities.

The informational-statistical-entropy operator in a nonequilibrium ensemble formalism

We study the eigenvalue spectrum of the informational-statistical-entropy operator, a quantity that plays a fundamental role in the nonequilibrium statistical operator method. We obtain explicit expressions for the informational entropy for inhomogeneous nonequilibrium (dissipative) systems, relevant for the study of its nonclassical nonlinear hydrodynamics. Expressions for the single-particle dynamical matrix and, in particular, for the distribution functions of quasi-particles, in conditions arbitrarily away from equilibrium, are also derived. We apply the results considering some aspects of the hydrodynamics of a Fermion system in weak interaction with a thermal bath of Bosons.

On the selection of the state space in nonequilibrium thermodynamics

We address here the question of the choice and interpretation of state variables in the thermodynamical description of systems arbitrarily away from equilibrium. It is presented a discussion of the topic in the framework of informational statistical thermodynamics, an approach based on Gibbs algorithm for nonequilibrium dissipative systems, which provides mechano-statistical foundations to phenomenological theories of irreversible thermodynamics. The theory is applied in the case of a particular system consisting of the mobile carriers in a highly excited photo-injected plasma in semiconductors. The concepts and results thus obtained are tested against experimental data in time-resolved and time-integrated optical laser spectroscopy. It is shown how equilibrium thermodynamic variables are evidenced and measured in such experiments. It is also discussed the influence on them of the inclusion of dissipative fluxes among the basic variables.

Time-reversible dissipative attractors in three and four phase-space dimensions

We establish the dissipative nature of several three- and four-dimensional time-reversible phase-space flows and study their ergodicity. Three- and four-dimensional generalizations of the equilibrium Nos\'e-Hoover oscillator provide the simplest robust continuous models for time-reversible nonequilibrium dissipative systems. Most such systems exhibit discontinuities or periodicities. We have discovered one set of four ordinary differential equations which is simultaneously robust, time-reversible, dissipative, and ergodic, with solutions free of any discontinuities and periodicities.

Self-organization in semiconductor physics

Non-equilibrium dissipative systems from semiconductor physics have prevailed as a paradigmatic testing field for complex non-linear dynamics during the last decade. Especially, low-temperature impact ionization breakdown in extrinsic germanium crystals displays a variety of interesting nonlinear phenomena, such as spontaneous oscillations and filamentary patterns of the current flow. We report on recent experimental results concerning the interplay between spatial and temporal degrees of freedom during the onset of semiconductor breakdown. Quantitative evaluation of characteristic scaling properties supports the applicability of the model of self-organized criticality.

An Extension of the Dynamical Mapping to Nonequilibrium Dissipative Systems

An Extension of the Dynamical Mapping to Nonequilibrium Dissipative Systems

DENSITY MATRIX FORMALISM, DOUBLE-SPACE AND THERMO FIELD DYNAMICS IN NON-EQUILIBRIUM DISSIPATIVE SYSTEMS

General relationship among the density matrix formalism, the double-space formulation and thermo field dynamics is discussed in non-equilibrium dissipative quantum systems. The concept of weakly equivalent operators in the double space formulation is introduced to review many well-known results and it is shown to be useful in mapping between the density matrix formalism and the double space formulation. A new non-equilibrium thermo field dynamics is formulated to discuss dissipative quantum systems. A simple example of damped harmonic oscillators is discussed in the present representation.

Spontaneous Symmetry Breaking and Nambu-Goldstone Mode in a Non-Equilibrium Dissipative System

Dans un etat stationnaire hors d'equilibre a structure d'espace-temps un mode de Nambu-Goldstone avec dissipation apparait comme une consequence de la rupture de symetrie spontanee