Fluctuation-dissipation Ratio Research Articles

Thermalization with a multibath: an investigation in simple models

We study analytically and numerically a couple of paradigmatic spin models, each described in terms of two sets of variables attached to two different thermal baths with characteristic timescales T and τ and inverse temperatures B and β. In the limit in which one bath becomes extremely slow (), such models amount to a paramagnet and to a one-dimensional ferromagnet in contact with a single bath. Our study is also motivated by analogies with disordered systems where widely separated timescales associated with different effective temperatures emerge. We show that these systems reach a stationary state in a finite time for any choice of B and β. We determine the non-equilibrium fluctuation-dissipation relation between the autocorrelation and the response function in such a state and, from that, we discuss if and how thermalization with the two baths occurs and the emergence of a non-trivial fluctuation-dissipation ratio.

Phase Separation and Correlated Motions in Motorized Genome.

The human genome is arranged in the cell nucleus nonrandomly, and phase separation has been proposed as an important driving force for genome organization. However, the cell nucleus is an active system, and the contribution of nonequilibrium activities to phase separation and genome structure and dynamics remains to be explored. We simulated the genome using an energy function parametrized with chromosome conformation capture (Hi-C) data with the presence of active, nondirectional forces that break the detailed balance. We found that active forces that may arise from transcription and chromatin remodeling can dramatically impact the spatial localization of heterochromatin. When applied to euchromatin, active forces can drive heterochromatin to the nuclear envelope and compete with passive interactions among heterochromatin that tend to pull them in opposite directions. Furthermore, active forces induce long-range spatial correlations among genomic loci beyond single chromosome territories. We further showed that the impact of active forces could be understood from the effective temperature defined as the fluctuation-dissipation ratio. Our study suggests that nonequilibrium activities can significantly impact genome structure and dynamics, producing unexpected collective phenomena.

Universal amplitudes ratios for critical aging via functional renormalization group

We discuss how to calculate non-equilibrium universal amplitude ratios in the functional renormalization group approach, extending its applicability. In particular, we focus on the critical relaxation of the Ising model with non-conserved dynamics (model A) and calculate the universal amplitude ratio associated with the fluctuation–dissipation ratio of the order parameter, considering a critical quench from a high-temperature initial condition. Our predictions turn out to be in good agreement with previous perturbative renormalization-group calculations and Monte Carlo simulations.

The Einstein effective temperature can predict the tagged active particle density.

We derive a distribution function for the position of a tagged active particle in a slowly varying in space external potential, in a system of interacting active particles. The tagged particle distribution has the form of the Boltzmann distribution but with an effective temperature that replaces the temperature of the heat bath. We show that the effective temperature that enters the tagged particle distribution is the same as the effective temperature defined through the Einstein relation, i.e., it is equal to the ratio of the self-diffusion and tagged particle mobility coefficients. This result shows that this effective temperature, which is defined through a fluctuation-dissipation ratio, is relevant beyond the linear response regime. We verify our theoretical findings through computer simulations. Our theory fails when an additional large length scale appears in our active system. In the system we simulated, this length scale is associated with long-wavelength density fluctuations that emerge upon approaching motility-induced phase separation.

Non-equilibrium critical behavior of the three-dimensional anisotropic Heisenberg model: dynamical susceptibility and fluctuation-dissipation ratio

Simulation of the non-equilibrium critical behavior of the three-dimensional anisotropic Heisenberg model is carried out with realization of Glauber dynamics and the dynamical susceptibility and the fluctuation-dissipation ratio are calculated with evolution of system from a high-temperature initial state.

Marginal Effect of Structural Defects on the Nonequilibrium Critical Behavior of the Two-Dimensional Ising Model

The influence of various initial magnetizations m0 and structural defects on the nonequilibrium critical behavior of the two-dimensional Ising model is numerically simulated by Monte Carlo methods. Based on analysis of the time dependence of magnetization and the two-time dependences of autocorrelation function and dynamic susceptibility, we revealed the influence of logarithmic corrections and the crossover phenomena of percolation behavior on the nonequilibrium characteristics and the critical exponents. Violation of the fluctuation–dissipation theorem is studied, and the limiting fluctuation–dissipation ratio is calculated for the case of high-temperature initial state. The influence of various initial states on the limiting fluctuation–dissipation ratio is investigated. The nonequilibrium critical dynamics of weakly disordered systems with spin concentrations p ≥ 0.9 is shown to belong to the universality class of the nonequilibrium critical behavior of the pure model and to be characterized by the same critical exponents and the same limiting fluctuation–dissipation ratios. The nonequilibrium critical behavior of systems with p ≤ 0.85 demonstrates that the universal characteristics of the nonequilibrium critical behavior depend on the defect concentration and the dynamic scaling is violated, which is related to the influence of the crossover effects of percolation behavior.

Peculiarities of non-equilibrium critical behavior of site-diluted 2D Ising model

The results of a numerical Monte Carlo study of features of nonequilibrium critical behavior in a two-dimensional pure and structurally disordered Ising models are presented with realization of evolution from different initial states within the wide range of spin concentrations p = 1.0, 0.95, 0.9, 0.85, 0.8, 0.75, and 0.7. Analysis of the two-time dependences of the autocorrelation function and dynamic susceptibility revealed a substantial influence of the initial states on the aging effects. The violation of the fluctuation-dissipation theorem is studied, and the asymptotic values of the fluctuation-dissipation ratio are calculated.

Influence of initial states and structure defects on non-equilibrium critical behavior of 3D and 2D Ising models

Results of Monte Carlo description of features of non-equilibrium critical behavior in three- and two-dimensional Ising models conditioned by presence of structural quenched disorder are presented. It was revealed that the increase in the concentration of defects is accompanied by the strengthening of the aging effects manifested as the slowing down of correlation and relaxation processes in structurally disordered systems as compared to the pure system. Non-equilibrium initial states begin to increasingly more strongly influence peculiar features and characteristics of the system’s evolution. It was shown that limiting fluctuation-dissipation ratio values X∞ characterizing the degree of system departure from equilibrium satisfy inequality X∞ < 1 and depend on the universality class of non-equilibrium critical behavior to which they belong: one of these classes corresponds to the high-temperature, and the other to the low-temperature initial state of the system. Values of these non-equilibrium characteristics in 3D Ising model demonstrate belonging to universality classes of critical behavior of weakly and strongly diluted systems, but non-equilibrium characteristics in 2D Ising model depend continuously on concentration of defects owing to the crossover effects in the percolation behavior.

Characterising the nonequilibrium stationary states of Ornstein–Uhlenbeck processes

We characterise the nonequilibrium stationary state of a generic multivariate Ornstein–Uhlenbeck process involving degrees of freedom. The irreversibility of the process is encoded in the antisymmetric part of the Onsager matrix. The linearity of the Langevin equations allows us to derive closed-form expressions in terms of the latter matrix for many quantities of interest, in particular the entropy production rate and the fluctuation–dissipation ratio matrix. This general setting is then illustrated by two classes of systems. First, we consider the one-dimensional ferromagnetic Gaussian spin model endowed with a stochastic dynamics where spatial asymmetry results in irreversibility. The stationary state on a ring is independent of the asymmetry parameter, whereas it depends continuously on the latter on an open chain. Much attention is also paid to finite-size effects, especially near the critical point. Second, we consider arrays of resistively coupled electrical circuits. The entropy production rate is evaluated in the regime where the local temperatures of the resistors have small fluctuations. For networks the entropy production rate grows linearly with the size of the array. For networks a quadratic growth law violating extensivity is predicted.

Fluctuation relations, effective temperature, and ageing of enzymes: The case of protein electron transfer

Proteins catalyzing chemical reactions are glassy systems in which the reaction time is often below the time of conformational relaxation. The protein is not able to sample its configuration space on the reaction time, leading to nonergodic ensemble averages. This phenomenology makes the effective configurational temperature of the protein significantly higher than the kinetic temperature of the bath. The effective temperature is expressed in terms of the fluctuation-dissipation ratio quantifying the violation of the fluctuation dissipation theorem (FDT). For reactions of protein electron transfer, the ratio of configurational and kinetic temperatures is given by the ratio of two reorganization energies related to, correspondingly, thermal fluctuations of the thermal bath and linear response of the bath to electron arriving to the active site. The violation of the FDT leads to a significant depression of the activation barrier achieved trough nonergodic exploration of the protein configuration space. The time of conformational dynamics, leading to equilibration, establishes the ageing time during which the enzyme has to be reset to its original configuration. Experimental evidence and numerical simulations indicate a factor of 2–3 violation of the FDT for protein electron transfer at physiological temperatures. Lowering temperature freezes the protein into a state consistent with the FDT through a glass transition. Design principles of physiological energy chains are discussed by postulating the need to maintain FDT violated to support catalytic function.

Monte Carlo Study of the Effect of Initial States and Structural Defects on Nonequilibrium Critical Behavior of the Three-Dimensional Ising Model

The effect of various initial magnetizations m0 and structural defects the nonequilibrium critical behavior of the three-dimensional Ising model is numerically studied. Based on an analysis of the time dependence of the magnetization and the two-time dependence of the autocorrelation function and dynamic susceptibility, the significant effect of initial states on relaxation magnetizations and aging effects characterized by anomalous relaxation inhibition and correlation in the system with increasing waiting time was revealed. The fluctuation–dissipation theorem violation was studied, and the values of the limit fluctuation–dissipation ratio (FDR) are calculated. It is shown that two universality subclasses can be distinguished in the nonequilibrium critical behavior of the three-dimensional Ising model with random initial magnetization m0 These subclasses correspond to the system evolution from the high-temperature (m0 = 0) and low-temperature (m0 = 1) initial states with limit FDRs characteristic of these states.

Superaging and Subaging Phenomena in a Nonequilibrium Critical Behavior of the Structurally Disordered Two-Dimensional XY Model

A Monte Carlo numerical simulation of the specific features of nonequilibrium critical behavior is carried out for the two-dimensional structurally disordered XY model during its evolution from a low-temperature initial state. On the basis of the analysis of the two-time dependence of autocorrelation functions and dynamic susceptibility for systems with spin concentrations of p = 1.0, 0.9, and 0.6, aging phenomena characterized by a slowing down of the relaxation system with increasing waiting time and the violation of the fluctuation–dissipation theorem (FDT) are revealed. The values of the universal limiting fluctuation–dissipation ratio (FDR) are obtained for the systems considered. As a result of the analysis of the two-time scaling dependence for spin–spin and connected spin autocorrelation functions, it is found that structural defects lead to subaging phenomena in the behavior of the spin–spin autocorrelation function and superaging phenomena in the behavior of the connected spin autocorrelation function.

Монте-Карло-исследование влияния начальных состояний и дефектов структуры на неравновесное критическое поведение трехмерной модели Изинга

AbstractThe effect of various initial magnetizations m _0 and structural defects the nonequilibrium critical behavior of the three-dimensional Ising model is numerically studied. Based on an analysis of the time dependence of the magnetization and the two-time dependence of the autocorrelation function and dynamic susceptibility, the significant effect of initial states on relaxation magnetizations and aging effects characterized by anomalous relaxation inhibition and correlation in the system with increasing waiting time was revealed. The fluctuation–dissipation theorem violation was studied, and the values of the limit fluctuation–dissipation ratio (FDR) are calculated. It is shown that two universality subclasses can be distinguished in the nonequilibrium critical behavior of the three-dimensional Ising model with random initial magnetization m _0 These subclasses correspond to the system evolution from the high-temperature ( m _0 = 0) and low-temperature ( m _0 = 1) initial states with limit FDRs characteristic of these states.

Analysis of the Effect of Different Initial States and Structural Defects on the Characteristics of the Nonequilibrium Critical Behavior of the 3D Ising Model

The effect of different initial values m0 of magnetization and structural defects on the nonequilibrium critical behavior of the 3D Ising model have been analyzed numerically using the Monte Carlo method. Analysis of the two-time dependences of the autocorrelation function and dynamic susceptibility has revealed a substantial influence of the initial states on the aging effects that are characterized by anomalous retardation of relaxation and correlation in the system upon an increase in the waiting time. We have studied the violations of the fluctuation–dissipation theorem and calculated the limiting fluctuation–dissipation ratio. It is shown that in the nonequilibrium critical behavior of the 3D Ising model, two universality subclasses corresponding to the evolution of the system from the high-temperature (with m0 = 0) and low-temperature (with m0 = 1) initial states with the values of the limiting fluctuation–dissipation ratio typical of these states can be singled out.

Driven Brownian particle as a paradigm for a nonequilibrium heat bath: Effective temperature and cyclic work extraction

We apply the concept of a frequency-dependent effective temperature based on the fluctuation-dissipation ratio to a driven Brownian particle in a nonequilibrium steady state. Using this system as a thermostat for a weakly coupled harmonic oscillator, the oscillator thermalizes according to a canonical distribution at the respective effective temperature across the entire frequency spectrum. By turning the oscillator from a passive thermometer into a heat engine, we realize the cyclic extraction of work from a single thermal reservoir, which is feasible only due to its nonequilibrium nature.

A statics-dynamics equivalence through the fluctuation–dissipation ratio provides a window into the spin-glass phase from nonequilibrium measurements

We have performed a very accurate computation of the nonequilibrium fluctuation-dissipation ratio for the 3D Edwards-Anderson Ising spin glass, by means of large-scale simulations on the special-purpose computers Janus and Janus II. This ratio (computed for finite times on very large, effectively infinite, systems) is compared with the equilibrium probability distribution of the spin overlap for finite sizes. Our main result is a quantitative statics-dynamics dictionary, which could allow the experimental exploration of important features of the spin-glass phase without requiring uncontrollable extrapolations to infinite times or system sizes.

Influence of disorder on ageing and memory effects in non-equilibrium critical dynamics of 3D Ising model relaxing from an ordered state

We have performed a numerical investigation of the influence of disorder on the dynamical non-equilibrium evolution of a 3D site-diluted Ising model from a low-temperature initial state with magnetization m0 = 1. It is shown that two-time dependences of the autocorrelation and integrated response functions for systems with spin concentrations p = 1.0, 0.95, 0.8, 0.6 and 0.5 demonstrate ageing properties with anomalous slowing-down relaxation and violation of the fluctuation-dissipation ratio. It was revealed that during non-equilibrium critical dynamics in the long-time regime the autocorrelation functions for diluted systems are extremely slow due to the pinning of domain walls on impurity sites. We have found that the fluctuation-dissipation ratio for diluted systems with spin concentration p < 1 while the pure system is characterized by . The autocorrelation function power-law delay becomes the same as for the time dependence of the magnetization in the critical point and is characterized by exponent . Also, for diluted systems we reveal memory effects for critical evolution in the ageing regime with realization of cyclic temperature change and quenching at .

Aging and memory effects in the nonequilibrium critical behavior of structurally disordered magnetic materials in the course of their evolution from the low-temperature initial state

The Monte Carlo study of the nonequilibrium critical evolution of structurally disordered anisotropic magnetic materials from the low-temperature initial state with the reduced magnetization m 0 = 1 is performed within the broad range of spin densities, p = 1.0, 0.95, 0.8, 0.6, and 0.5. It is shown that, in such systems, the pinning of domain walls by structural defects occurring when the evolution starts from the low-temperature state leads to significant changes in the nonequilibrium “aging” and “memory” effects in comparison to those characteristic of the “pure” system. As a result, in the long-term regime at times t–t w » t w » 1, an anomalously strong slowing down in the correlation effects is revealed. It is shown that a decrease in the autocorrelation function with time occurs according to a power law typical of the critical relaxation of the magnetization in contrast to a usual scaling dependence. Eventually, the limiting value of the fluctuation–dissipation ratio X∞ for the structurally disordered systems with p < 1 vanishes, whereas for the pure system, we have X∞ = 0.784(5). The nonequilibrium critical “superaging” stage is found. This stage is characterized by the critical exponent µ = 2.30(6) for weakly disordered systems and by µ = 2.80(7) for the systems with strong disorder.

Nonequilibrium aging effects in the critical behavior of structurally disordered planar magnets

Nonequilibrium critical behavior of structurally disordered planar magnets described by the two-dimensional XY model has been studied by Monte Carlo methods. For systems evolving from a high-temperature nonequilibrium initial state, the influence of defects of the structure on aging effects, as well as the violation of the fluctuation-dissipation theorem for “freezing” temperatures in the low-temperature phase, has been analyzed. Power-law temperature dependences of the limiting values of the fluctuation-dissipation ratio have been revealed for the first time.

Ageing and non-equilibrium critical phenomena in Monte Carlo simulations

It is considered the non-equilibrium critical evolution of statistical systems which displays some features, such as ageing and violation of the fluctuation-dissipation theorem. We review here some theoretical results of computations that have been obtained in recent years for universal quantities, such as the exponents determining the scaling behaviour of dynamic response and correlation functions and the fluctuation-dissipation ratio, associated with the non-equilibrium critical dynamics, with particular focus on the 3D pure and diluted Ising models with Glauber dynamics. We analyse an influence of critical fluctuations, different non-equilibrium initial states and presence of nonmagnetic impurities in spin systems on two-time dependence of correlation and response functions on characteristic time variables as waiting time tw and time of observation t – tw with t > tw. We discuss the obtained values of non-equilibrium exponents for autocorrelation and response functions and values of the universal long-time limit of the fluctuation-dissipation ratio X∞. Analysis of simulation results show that the insertion of disorder leads to new values of X∞ with X∞diluted > X∞pure.