Violation Of Fluctuation-dissipation Theorem Research Articles

Violation of the fluctuation-dissipation theorem and effective temperatures in spin ice

We present numerical tests of the fluctuation-dissipation theorem (FDT) in the dumbbell model of spin ice with parameters suitable for dysprosium titanate. The tests are made for local spin variables, magnetic monopole density, and energy. We are able to achieve local equilibrium in which the FDT is satisfied down to $T=0.4$ K below which the system completely freezes. Non-equilibrium dynamics, together with violation of the FDT, are nonetheless observed following a thermal quench into the non-contractable monopole pair regime. Despite FDT violation, an approximate linear response regime allows for the identification of effective non-equilibrium temperatures which are different for each variable. The spin variable appears hotter than the heat reservoir, the monopole concentration responds with a lower effective temperature while the energy has a negative effective temperature. Results are discussed in the context of the monopole picture of spin ice and compared to the structure of FDT violations in other glassy materials. Prospectives for future experiments are reviewed.

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.

Inferring energy dissipation from violation of the fluctuation-dissipation theorem.

The Harada-Sasa equality elegantly connects the energy dissipation rate of a moving object with its measurable violation of the Fluctuation-Dissipation Theorem (FDT). Although proven for Langevin processes, its validity remains unclear for discrete Markov systems whose forward and backward transition rates respond asymmetrically to external perturbation. A typical example is a motor protein called kinesin. Here we show generally that the FDT violation persists surprisingly in the high-frequency limit due to the asymmetry, resulting in a divergent FDT violation integral and thus a complete breakdown of the Harada-Sasa equality. A renormalized FDT violation integral still well predicts the dissipation rate when each discrete transition produces a small entropy in the environment. Our study also suggests a way to infer this perturbation asymmetry based on the measurable high-frequency-limit FDT violation.

Topological properties of the limited penetrable horizontal visibility graph family.

The limited penetrable horizontal visibility graph algorithm was recently introduced to map time series in complex networks. In this work, we extend this algorithm to create a directed-limited penetrable horizontal visibility graph and an image-limited penetrable horizontal visibility graph. We define two algorithms and provide theoretical results on the topological properties of these graphs associated with different types of real-value series. We perform several numerical simulations to check the accuracy of our theoretical results. Finally, we present an application of the directed-limited penetrable horizontal visibility graph to measure real-value time series irreversibility and an application of the image-limited penetrable horizontal visibility graph that discriminates noise from chaos. We also propose a method to measure the systematic risk using the image-limited penetrable horizontal visibility graph, and the empirical results show the effectiveness of our proposed algorithms.

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.

Quantum violation of fluctuation-dissipation theorem

We study quantum measurements of temporal equilibrium fluctuations in macroscopic quantum systems. It is shown that the fluctuation-dissipation theorem, as a relation between observed quantities, is partially violated in quantum systems, even if measurements are made in an ideal way that emulates classical ideal measurements as closely as possible. This is a genuine quantum effect that survives on a macroscopic scale. We also show that the state realized during measurements of temporal equilibrium fluctuations is a ‘squeezed equilibrium state’, which is macroscopically identical to the pre-measurement equilibrium state but is squeezed by the measurement. It is a time-evolving state, in which macrovariables fluctuate and relax. We also explain some of subtle but important points, careless treatments of which often lead to unphysical results, of the linear response theory.

Theory of driven nonequilibrium critical phenomena

A system driven in the vicinity of its critical point by varying a relevant field in an arbitrary function of time is a generic system that possesses a long relaxation time compared with the driving time scale and thus represents a large class of nonequilibrium systems. For such a manifestly nonlinear nonequilibrium strongly fluctuating system, we show that there exists universal nonequilibrium critical behavior that is well described incredibly by its equilibrium critical properties. A dynamic renormalization-group theory is developed to account for the behavior. The weak driving may give rise to several time scales depending on its form and thus rich nonequilibrium phenomena of various regimes and their crossovers, negative susceptibilities, as well as violation of fluctuation-dissipation theorem. An initial condition that can be in either equilibrium or nonequilibrium but has longer correlations than the driving scales also results in a unique regime and complicates the situation. Implication of the results on measurement is also discussed. The theory may shed light on study of other nonequilibrium systems and even nonlinear science.

Ageing properties of three-dimensional pure and site-diluted Ising ferromagnets

Ageing properties of the three-dimensional pure and diluted Ising models are investigated for case with quenching from a high temperature initial state to their critical points. The two-times autocorrelation and response functions for the systems with spin concentrations p = 1.0, 0.8, and 0.6 are computed and analysed. The fluctuation-dissipation theorem violation for considered 3D Ising models are shown with the asymptotic values of the fluctuation-dissipation ratio X∞(p) < 1/2. The asymptotic values of universal fluctuation-dissipation ratio X∞ were measured, and it was shown that X∞disorder(p < 1) > X∞pure(p = 1).

Nonequilibrium and information: The role of cross correlations

We discuss the relevance of information contained in cross correlations among different degrees of freedom, which is crucial in nonequilibrium systems. In particular we consider a stochastic system where two degrees of freedom X{1} and X{2}-in contact with two different thermostats-are coupled together. The production of entropy and the violation of equilibrium fluctuation-dissipation theorem (FDT) are both related to the cross correlation between X{1} and X{2}. Information about such cross correlation may be lost when single-variable reduced models for X_{1} are considered. Two different procedures are typically applied: (a) one totally ignores the coupling with X{2}; and (b) one models the effect of X{2} as an average memory effect, obtaining a generalized Langevin equation. In case (a) discrepancies between the system and the model appear both in entropy production and linear response; the latter can be exploited to define effective temperatures, but those are meaningful only when time scales are well separated. In case (b) linear response of the model well reproduces that of the system; however the loss of information is reflected in a loss of entropy production. When only linear forces are present, such a reduction is dramatic and makes the average entropy production vanish, posing problems in interpreting FDT violations.

Effects of error on fluctuations under feedback control

We consider a one-dimensional brownian motion under nonequilibrium feedback control. Generally, the fluctuation-dissipation theorem (FDT) is violated in driven systems under nonequilibrium conditions. We find that the degree of the FDT violation is bounded by the mutual information obtained by the feedback system when the feedback protocol includes measurement errors. We introduce two simple models to illustrate cooling processes by feedback control and demonstrate analytical results for the cooling limit in those systems. Especially in a steady state, lower bounds to the effective temperature are given by an inequality similar to the Carnot efficiency.

Experimental Evidence for Violation of the Fluctuation-Dissipation Theorem in a Superspin Glass

We present the experimental observation of the fluctuation-dissipation theorem violation in an assembly of interacting magnetic nanoparticles in the low temperature superspin-glass phase. The magnetic noise is measured with a two-dimension electron gas Hall probe and compared to the out of phase ac susceptibility of the same ferrofluid. For "intermediate" aging times of the order of 1 h, the ratio of the effective temperature T(eff) to the bath temperature T grows from 1 to 6.5 when T is lowered from T(g) to 0.3 T(g), regardless of the noise frequency. These values are comparable to those measured in an atomic spin glass as well as those calculated for a Heisenberg spin glass.

Nonequilibrium fluctuation-dissipation relations of interacting Brownian particles driven by shear

We present a detailed analysis of the fluctuation-dissipation theorem (FDT) close to the glass transition in colloidal suspensions under steady shear using mode coupling approximations. Starting point is the many-particle Smoluchowski equation. Under shear, detailed balance is broken and the response functions in the stationary state are smaller at long times than estimated from the equilibrium FDT. An asymptotically constant relation connects response and fluctuations during the shear driven decay, restoring the form of the FDT with, however, a ratio different from the equilibrium one. At short times, the equilibrium FDT holds. We follow two independent approaches whose results are in qualitative agreement. To discuss the derived fluctuation-dissipation ratios, we show an exact reformulation of the susceptibility which contains not the full Smoluchowski operator as in equilibrium, but only its well defined Hermitian part. This Hermitian part can be interpreted as governing the dynamics in the frame comoving with the probability current. We present a simple toy model which illustrates the FDT violation in the sheared colloidal system.

Nonequilibrium dynamics in an amorphous solid

The nonequilibrium dynamics of an amorphous solid is studied with a soft-spin model. We show that the aging behavior in the glassy state follows a modified Kohlrausch-Williams-Watts form similar to that obtained in Lunkenheimer [Phys. Rev. Lett. 95, 055702 (2005)] from analysis of the dielectric loss data. The nature of the fluctuation-dissipation theorem violation is also studied in time as well as correlation windows.

2P-310 F_1-ATPase 1分子の揺動散逸定理の破れの測定(非平衡/生体リズム,第46回日本生物物理学会年会)

2P-310 F_1-ATPase 1分子の揺動散逸定理の破れの測定(非平衡/生体リズム,第46回日本生物物理学会年会)

Violation of the Fluctuation-Dissipation Theorem and Heating Effects in the Time-Dependent Kondo Model

The fluctuation-dissipation theorem (FDT) plays a fundamental role in understanding quantum many-body problems. However, its applicability is limited to equilibrium systems and it does in general not hold in nonequilibrium situations. This violation of the FDT is an important tool for studying nonequilibrium physics. In this paper we present results for the violation of the FDT in the Kondo model where the impurity spin is frozen for all negative times, and set free to relax at positive times. We derive exact analytical results at the Toulouse point, and results within a controlled approximation in the Kondo limit, which allow us to study the FDT violation on all time scales.A measure of the FDT violation is provided by the effective temperature, which shows initial heating effects after switching on the perturbation, and then exponential cooling to zero temperature as the Kondo system reaches equilibrium.

Fluctuation-dissipation relations in the nonequilibrium critical dynamics of Ising models.

We investigate the relation between two-time multispin correlation and response functions in the nonequilibrium critical dynamics of Ising models in d=1 and d=2 spatial dimensions. In these nonequilibrium situations, the fluctuation-dissipation theorem (FDT) is not satisfied. We find FDT "violations" qualitatively similar to those reported in various glassy materials, but quantitatively dependent on the chosen observable, in contrast to the results obtained in infinite-range glass models. Nevertheless, all FDT violations can be understood by considering separately the contributions from large wave vectors, which are at quasiequilibrium and obey the FDT, and from small wave vectors where a generalized FDT holds with a nontrivial fluctuation-dissipation ratio X infinity. In d=1, we get X(infinity)=1/2 for spin observables, which measure the orientation of domains, while X(infinity)=0 for observables that are sensitive to the domain-wall motion. Numerical simulations in d=2 reveal a unique X infinity approximately equal 0.34 for all observables. Measurement protocols for X infinity are discussed in detail. Our results suggest that the definition of an effective temperature T(eff)=T/X(infinity) for large length scales is generically possible in nonequilibrium critical dynamics.

Glass and polycrystal states in a lattice spin model

We numerically study a nondisordered lattice spin system with a first order liquid–crystal transition, as a model for supercooled liquids and glasses. Below the melting temperature the system can be kept in the metastable liquid phase, and it displays a dynamic phenomenology analogous to fragile supercooled liquids, with stretched exponential relaxation, power law increase of the relaxation time, and high fragility index. At an effective spinodal temperature Tsp the relaxation time exceeds the crystal nucleation time, and the supercooled liquid loses stability. Below Tsp liquid properties cannot be extrapolated, in line with Kauzmann’s scenario of a lower metastability limit of supercooled liquids as a solution of Kauzmann’s paradox. The off-equilibrium dynamics below Tsp corresponds to fast nucleation of small, but stable, crystal droplets, followed by extremely slow growth, due to the presence of pinning energy barriers. In the early time region, which is longer the lower the temperature, this crystal-growth phase is indistinguishable from an off-equilibrium glass, both from a structural and a dynamical point of view: crystal growth has not advanced enough to be structurally detectable, and a violation of the fluctuation–dissipation theorem (FDT) typical of structural glasses is observed. On the other hand, for longer times crystallization reaches a threshold beyond which crystal domains are easily identified, and FDT violation becomes compatible with ordinary domain growth.

Observation of Fluctuation-Dissipation-Theorem Violations in a Structural Glass

The fluctuation-dissipation theorem (FDT), connecting dielectric susceptibility and polarization noise, was studied in glycerol below its glass transition temperature ${T}_{g}$. Weak FDT violations were observed after a quench from just above to just below ${T}_{g}$, for frequencies above the $\ensuremath{\alpha}$ peak. Violations persisted up to ${10}^{5}$ times the thermal equilibration time of the configurational degrees of freedom under study, but comparable to the average relaxation time of the material. These results suggest that excess energy flows from slower to faster relaxing modes.

Violation of the fluctuation-dissipation theorem in a two-dimensional Ising model with dipolar interactions

The violation of the Fluctuation-Dissipation Theorem (FDT) in a two-dimensional Ising model with both ferromagnetic exchange and antiferromagnetic dipolar interactions is established and investigated via Monte Carlo simulations. Through the computation of the autocorrelation C(t+t_w,t_w) and the integrated response (susceptibility) functions we obtain the FDT violation factor X(t+t_w,t_w) for different values of the temperature, the waiting time t_w and the quotient delta=J_0/J_d, J_0 and J_d being the strength of exchange and dipolar interactions respectively. For positive values of delta this system develops a striped phase at low temperatures, in which the non-equilibrium dynamics presents two different regimes. Our results show that such different regimes are not reflected in the FDT violation factor, where X goes always to zero for high values of t_w in the aging regime, a result that appears in domain growth processes in non-frustrated ordered systems.

Violation of the fluctuation-dissipation theorem in finite-dimensional spin glasses

We study the violation of the fluctuation-dissipation theorem in the three and four dimensional Gaussian Ising spin glasses using on and off equilibrium simulations. We have characterized numerically the function X(C) that determine the violation and we have studied its scaling properties. Moreover we have computed the function x(C) which characterize the breaking of the replica symmetry directly from equilibrium simulations. The two functions are numerically equal and in this way we have established that the conjectured connection between the violation of fluctuation dissipation theorem in the off-equilibrium dynamics and the replica symmetry breaking at equilibrium holds for finite dimensional spin glasses. These results point to a spin glass phase with spontaneously broken replica symmetry in finite dimensional spin glasses.