Large fluctuations in driven dissipative media

We analyze the fluctuations of the dissipated energy in a simple and general model where dissipation, diffusion, and driving are the key ingredients. The full dissipation distribution, which follows from hydrodynamic fluctuation theory, shows non-Gaussian tails and no negative branch, thus violating the fluctuation theorem as expected from the irreversibility of the dynamics. It exhibits simple scaling forms in the weak- and strong-dissipation limits, with large fluctuations favored in the former case but strongly suppressed in the latter. The typical path associated with a given dissipation fluctuation is also analyzed in detail. Our results, confirmed in extensive simulations, strongly support the validity of hydrodynamic fluctuation theory to describe fluctuating behavior in driven dissipative media.     

Vortices in the Two-Dimensional Simple Exclusion Process

We show that the fluctuations of the partial current in two dimensional diffusive systems are dominated by vortices leading to a different scaling from the one predicted by the hydrodynamic large deviation theory. This is supported by exact computations of the variance of partial current fluctuations for the symmetric simple exclusion process on general graphs. On a two-dimensional torus, our exact expressions are compared to the results of numerical simulations. They confirm the logarithmic dependence on the system size of the fluctuations of the partial flux. The impact of the vortices on the validity of the fluctuation relation for partial currents is also discussed in an Appendix.     

Experimental test of the fluctuation theorem for a driven two-level system with time-dependent rates

A single defect center in diamond periodically excited by a laser is shown to provide a simple realization for a system obeying a fluctuation theorem for nonthermal noise. The distribution of these fluctuations is distinctly non-Gaussian, which has also been verified by numerical calculation. For driving protocols symmetric under time reversal a more restricted form of the theorem holds, which is also known from entropy fluctuations caused by thermal noise.     

Extension of the fluctuation theorem

Heat fluctuations are studied in a dissipative system with both deterministic and stochastic components for a simple model: a Brownian particle dragged through water by a moving potential. An extension of the stationary state fluctuation theorem is derived. For infinite time, this reduces to the conventional fluctuation theorem only for small fluctuations; for large fluctuations, it gives a much larger ratio of the probabilities of the particle to absorb rather than supply heat. This persists for finite times and should be observable in experiments similar to a recent one carried out by Wang et al.     

Linear response and fluctuation theorems for nonstationary stochastic processes

Linear response theory is developed for nonstationary Markov processes. A generalized fluctuation theorem is derived which relates the response function to a correlation of fluctuations of the unperturbed nonstationary process. It is shown that it reduces to an ordinary fluctuation theorem relating the response function to the two-point correlation between fluctuations of state variables in the case of a Gaussian distribution function. The results are illustrated by explicit calculation for the class of nonstationary linear Fokker-Planck processes.Supported by Schweizerischer Nationalfonds.     

Toy model of hydrodynamic fluctuations

We study hydrodynamic fluctuations in an ideal gas. Because one is interested in thermodynamic properties of small volume elements, Einstein's theory of equilibrium fluctuations in large systems is insufficient. A toy model of correlated fluctuations in neighboring small cells leads us to the distinction of biased and unbiased momentum densities. Hydrodynamic equations that satisfy the fluctuation-dissipation theorem can then be formulated in terms of these two different momentum densities or velocities.     

Effects of imperfect premixing coupled with hydrodynamic instability on flame propagation

The problem of flame propagation in imperfectly premixed mixtures—mixtures of reactants with variable composition—is considered in this numerical study. We carry out two-dimensional direct numerical simulations of a flame propagating in a globally lean fuel-oxidizer mixture with imposed velocity and composition fluctuations of various intensities. The configuration adopted is that of a flame front interacting with spatially evolving fluctuations, and the characteristic scales of the domain and of the fluctuations imposed are significantly larger than the characteristic thickness of the flame, to account for important flame dynamics such as the hydrodynamic instability. One-step chemistry and Fick’s diffusion law are considered, along with unity Lewis number assumption for all the species. It is observed, in agreement with previous results, that relatively weak fluctuations in composition alone may lead to a large increase in flame length and burning rate. The hydrodynamic instability caused by gas expansion, catalyzed by the composition fluctuations interacting with the flame, is found to be responsible for the flame length enhancement. It is observed as well that the relative importance of this effect diminishes as the velocity fluctuations present become more intense, and that composition fluctuations have a small impact on flame length for these cases. It is additionally found that, with increasing intensity of composition fluctuations, there is eventually a reduction of burning rate per unit length of flame which leads, consequently, to a weak reduction of overall burning rate for the largest velocity fluctuation intensities covered by this study.     

Fluidized granular medium as an instance of the fluctuation theorem

We study the statistics of the power flux into a collection of inelastic beads maintained in a fluidized steady state by external mechanical driving. The power shows large fluctuations, including frequent large negative fluctuations, about its average value. The relative probabilities of positive and negative fluctuations in the power flux are in close accord with the fluctuation theorem of Gallavotti and Cohen, even at time scales shorter than those required by the theorem. We also compare an effective temperature that emerges from this analysis to the kinetic granular temperature.     

A Nonequilibrium Extension of the Clausius Heat Theorem

We generalize the Clausius (in)equality to overdamped mesoscopic and macroscopic diffusions in the presence of nonconservative forces. In contrast to previous frameworks, we use a decomposition scheme for heat which is based on an exact variant of the Minimum Entropy Production Principle as obtained from dynamical fluctuation theory. This new extended heat theorem holds true for arbitrary driving and does not require assumptions of local or close to equilibrium. The argument remains exactly intact for diffusing fields where the fields correspond to macroscopic profiles of interacting particles under hydrodynamic fluctuations. We also show that the change of Shannon entropy is related to the antisymmetric part under a modified time-reversal of the time-integrated entropy flux.     

Exchange fluctuation theorems for a chain of interacting particles in presence of two heat baths

The exchange fluctuation theorem for heat exchanged between two systems at different temperatures, when kept in direct contact, has been investigated by Jarzynski and Wójcik [Phys. Rev. Lett. 92, 230602 (2004)]. We extend this result to the case where two Langevin reservoirs at different temperatures are connected via a conductor made of interacting particles, and are subjected to an external drive or work source. The Langevin reservoirs are characterized by Gaussian white noise fluctuations and concomitant friction coefficients. We first derive the Crooks theorem for the ratio between forward and reverse paths, and discuss the first law in this model. Then we derive the modified detailed fluctuation theorems (MDFT) for the heat exchanged at each end. These theorems differ from the usual form of the detailed fluctuation theorems (DFT) in literature, due the presence of an extra multiplicative factor. This factor quantifies the deviation of our MFDT from the DFT. Finally, we numerically study our model, with only two interacting particles for simplicity.     

Additive noise-induced Turing transitions in spatial systems with application to neural fields and the Swift-Hohenberg equation

This work studies the spatio-temporal dynamics of a generic integral-differential equation subject to additive random fluctuations. It introduces a combination of the stochastic center manifold approach for stochastic differential equations and the adiabatic elimination for Fokker-Planck equations, and studies analytically the systems’ stability near Turing bifurcations. In addition two types of fluctuation are studied, namely fluctuations uncorrelated in space and time, and global fluctuations, which are constant in space but uncorrelated in time. We show that the global fluctuations shift the Turing bifurcation threshold. This shift is proportional to the fluctuation variance. Applications to a neural field equation and the Swift-Hohenberg equation reveal the shift of the bifurcation to larger control parameters, which represents a stabilization of the system. All analytical results are confirmed by numerical simulations of the occurring mode equations and the full stochastic integral-differential equation. To gain some insight into experimental manifestations, the sum of uncorrelated and global additive fluctuations is studied numerically and the analytical results on global fluctuations are confirmed qualitatively.     

On the Asymptotic Convergence of the Transient and Steady-State Fluctuation Theorems

Nonequilibrium molecular dynamics simulations are used to demonstrate the asymptotic convergence of the transient and steady-state forms of the fluctuation theorem. In the case of planar Poiseuille flow, we find that the transient form, valid for all times, converges to the steady-state predictions on microscopic time scales. Further, we find that the time of convergence for the two theorems coincides with the time required for satisfaction of the asymptotic steady-state fluctuation theorem.     

Fluctuation theorem for stochastic systems

The fluctuation theorem describes the probability ratio of observing trajectories that satisfy or violate the second law of thermodynamics. It has been proved in a number of different ways for thermostatted deterministic nonequilibrium systems. In the present paper we show that the fluctuation theorem is also valid for a class of stochastic nonequilibrium systems. The theorem is therefore not reliant on the reversibility or the determinism of the underlying dynamics. Numerical tests verify the theoretical result.     

Enhanced observation of number fluctuations by use of structured light

The point statistics of light scattered from structured, incoherent illumination of a random and fluctuating population of identical scatterers are derived. Theoretical predictions for a two-beam illumination pattern in which the relative beam intensity is modulated are compared with computer simulations and experiments performed by illumination of a rotating mask of identical but random apertures. The use of structured light is found to enhance the size of fluctuations, and quantitative comparisons between theory and practical measurement are made. The structured-light technique introduces flexibility in fluctuation measurement, permitting optimal control of the dynamic range, and is relevant to the development of instrumentation for particle and flow analysis.     

Spontaneous symmetry breaking at the fluctuating level

Phase transitions not allowed in equilibrium steady states may happen, however, at the fluctuating level. We observe for the first time this striking and general phenomenon measuring current fluctuations in an isolated diffusive system. While small fluctuations result from the sum of weakly correlated local events, for currents above a critical threshold the system self-organizes into a coherent traveling wave which facilitates the current deviation by gathering energy in a localized packet, thus breaking translation invariance. This results in Gaussian statistics for small fluctuations but non-Gaussian tails above the critical current. Our observations, which agree with predictions derived from hydrodynamic fluctuation theory, strongly suggest that rare events are generically associated with coherent, self-organized patterns which enhance their probability.     

空间光通信的到达角起伏实验研究

 2006年上半年进行了距离为3 200 m的光束传输实验,对到达角起伏进行了24 h昼夜观测。实验中,每分钟进行一次连续测量,每次以1 kHz的信号采样频率连续采集10 s,得到10 000个到达角起伏实验数据,并反映了0.2~500 Hz频段的信息。根据高采样频率下的到达角起伏昼夜观测数据,分析了到达角起伏效应,并通过到达角起伏时间平滑因子,对曝光时间的平滑作用进行了研究。昼夜观测实验结果表明：在天气阴霾、能见度低的情况下,到达角起伏会显著减小;在强湍流区,到达角起伏出现饱和效应,在弱湍流区,到达角起伏的强度随着湍流强度的增加而增强;到达角起伏幅度随着曝光时间的增加而减小,由归一化协方差拟合关系得到的时间平滑因子计算结果与实验直接分析得到的结果一致。     

From 1/f noise to multifractal cascades in heartbeat dynamics

We explore the degree to which concepts developed in statistical physics can be usefully applied to physiological signals. We illustrate the problems related to physiologic signal analysis with representative examples of human heartbeat dynamics under healthy and pathologic conditions. We first review recent progress based on two analysis methods, power spectrum and detrended fluctuation analysis, used to quantify long-range power-law correlations in noisy heartbeat fluctuations. The finding of power-law correlations indicates presence of scale-invariant, fractal structures in the human heartbeat. These fractal structures are represented by self-affine cascades of beat-to-beat fluctuations revealed by wavelet decomposition at different time scales. We then describe very recent work that quantifies multifractal features in these cascades, and the discovery that the multifractal structure of healthy dynamics is lost with congestive heart failure. The analytic tools we discuss may be used on a wide range of physiologic signals. (c) 2001 American Institute of Physics.     

Linear response domain in glassy systems

Molecular dynamics simulations are performed on a realistic glass forming model system. The linear and nonlinear response domains are explored numerically for the case where one of the particles interacts with a constant external force. As the temperature is lowered towards the glass transition, we find that the range of fields over which the response is linear shrinks towards zero. We show that the time required for convergence of the steady state fluctuation theorem and the valid application of the central limit theorem becomes very large as the glass transition is approached. This in turn implies that the domain over which a linear response can be observed becomes progressively smaller.     

Fluctuation Theorems for Entropy Production and Heat Dissipation in Periodically Driven Markov Chains

Asymptotic fluctuation theorems are statements of a Gallavotti-Cohen symmetry in the rate function of either the time-averaged entropy production or heat dissipation of a process. Such theorems have been proved for various general classes of continuous-time deterministic and stochastic processes, but always under the assumption that the forces driving the system are time independent, and often relying on the existence of a limiting ergodic distribution. In this paper we extend the asymptotic fluctuation theorem for the first time to inhomogeneous continuous-time processes without a stationary distribution, considering specifically a finite state Markov chain driven by periodic transition rates. We find that for both entropy production and heat dissipation, the usual Gallavotti-Cohen symmetry of the rate function is generalized to an analogous relation between the rate functions of the original process and its corresponding backward process, in which the trajectory and the driving protocol have been time-reversed. The effect is that spontaneous positive fluctuations in the long time average of each quantity in the forward process are exponentially more likely than spontaneous negative fluctuations in the backward process, and vice-versa, revealing that the distributions of fluctuations in universes in which time moves forward and backward are related. As an additional result, the asymptotic time-averaged entropy production is obtained as the integral of a periodic entropy production rate that generalizes the constant rate pertaining to homogeneous dynamics.     

Heat fluctuations in a nonequilibrium bath

We measure the energy fluctuations of a Brownian particle confined by an optical trap in an aging gelatin after a very fast quench (less than 1 ms). The strong nonequilibrium fluctuations due to the assemblage of the gel are interpreted, within the framework of fluctuation theorem, as a heat flux from the particle towards the bath. We derive an analytical expression of the heat probability distribution, which fits the experimental data and satisfies a fluctuation relation similar to that of a system in contact with two baths at different temperatures.