Fluctuation-dissipation theorem for metastable systems

We show that an appropriately defined fluctuation-dissipation theorem, connecting generalized susceptibilities and time correlation functions, is valid for times shorter than the nucleation time of the metastable state of Markovian systems satisfying detailed balance. This is done by assuming that such systems can be described by a superposition of the ground and first excited states of the master equation. We corroborate our results numerically for the metastable states of a two-dimensional Ising model.     

Fluctuation-dissipation theorem and the dynamical renormalization group

The relation between a recently introduced dynamical real-space renormalization group and the fluctuation-dissipation theorem is discussed. An apparent incompatibility is pointed out and resolved.     

Fluctuation-dissipation theorem in an aging colloidal glass

We provide a direct experimental test of the fluctuation-dissipation theorem (FDT) in an aging colloidal glass. The use of combined active and passive microrheology allows us to independently measure both the correlation and response functions in this nonequilibrium situation. Contrary to previous reports, we find no deviations from the FDT over several decades in frequency (1 Hz-10 kHz) and for all aging times. In addition, we find two distinct viscoelastic contributions in the aging glass, including a nearly elastic response at low frequencies that grows during aging.     

Fluctuation-dissipation theorem for a class of stationary open systems

A generalized fluctuation-dissipation theorem is proved in the frame of a Liouville-space formalism for stationary open systems in contact with reservoirs, and in general far from thermal equilibrium. It is shown, however, that the wellknown case of thermal equilibrium is included in the result.     

Fluctuation-dissipation theorem in liquid and glassy glycerol: frequency-dependent dielectric permittivity and dielectric polarization fluctuation measurements

We show frequency-dependent dielectric permittivity and dielectric polarization fluctuation measurements of liquid and glassy glycerol. This allows a direct comparison of both quantities determined independently. After cooling the glycerol sample to 179 K with a cooling rate of 0.85 K/min we studied the aging time dependence of the dielectric permittivity and the polarization fluctuations using the identical glycerol sample. A cross-correlation technique allows measurements of noise levels below the amplifier noise. In the frequency range between 0.3 and 300 Hz we find the measured data to be in agreement with the fluctuation-dissipation theorem for the liquid and glassy state not depending on the aging time.     

Fluctuation-dissipation ratio of the Heisenberg spin glass

The fluctuation-dissipation (FD) relation of the three-dimensional Heisenberg spin glass with weak random anisotropy is studied by off-equilibrium Monte Carlo simulation. The numerically determined FD ratio exhibits a "one-step-like" behavior, the effective temperature of the spin-glass state being about twice the spin-glass transition temperature, T(eff) approximately 2T(g), irrespective of the bath temperature. The results are discussed in conjunction with the recent experiment by Hérisson and Ocio, and with the chirality scenario of the spin-glass transition.     

Fluctuation-dissipation theorems for systems in non-thermal equilibrium and applications

The linear response theory of systems obeying Fokker-Planck equations is discussed under the assumption that the principle of detailed balance is satisfied. This theory is used to obtain fluctuation-dissipation theorems for systems in a non-thermal equilibrium state corresponding to the steady state solution of the Fokker-Planck equation. Some of the aspects of the threshold region of a single mode laser (without detuning) are discussed. In particular it is shown that, contrary to the results established recently by others, the “linear susceptibility” χ(Ω) is acontinuous function of the pump parameterp. The results are then specialized to Gaussian Markov process in which case an alternate form of the fluctuation-dissipation theorems is also given. Finally few other generalizations of the fluctuation-dissipation theorems are also briefly discussed.     

Fluctuation-dissipation models of a nonlinear resistor and Gupta's formulas

Moscow State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 31, No. 2, pp. 222–230, February, 1988.     

Fluctuation-dissipation relations and energy landscape in an out-of-equilibrium strong-glass-forming liquid

We study the out-of-equilibrium dynamics following a temperature jump in a model for silica, a strong liquid, and compare it with the well known case of fragile liquids. We calculate the fluctuation-dissipation relation, from which it is possible to estimate an effective temperature T(eff) associated with the slow out-of-equilibrium structural degrees of freedom. We find the striking and unexplained result that, different from the fragile liquid cases, T(eff) is smaller than the bath temperature.     

Fluctuation-dissipation relations in the activated regime of simple strong-glass models

We study the out-of-equilibrium fluctuation-dissipation (FD) relations in the low-temperature, finite-time, physical-aging regime of two simple models with strong glass behavior, the Fredrickson-Andersen model and the square-plaquette interaction model. We explicitly show the existence of unique, waiting-time independent dynamical FD relations. While in the Fredrickson-Andersen model the FD theorem is obeyed at all times, the plaquette model displays piecewise-linear FD relations, similar to what is found in disordered mean-field models and in simulations of supercooled liquids, and despite the fact that its static properties are trivial. We discuss the wider implications of these results.     

Conditions of stochasticity of two-dimensional billiards

There are two known mechanisms that produce chaos in billiard systems. The first one, discovered by Ya. G. Sinai, is called dispersing, the second, found by the author, is called defocusing. The same mechanisms produce chaos for geodesic flows. Some results on two-dimensional billiards, which indicate that only these two mechanisms can produce chaos in Hamiltonian systems, are discussed.     

Levelstatistics and stochasticity in a driven quantum system

We investigate quantum properties of one anisotropic spin driven by an external time-dependent magnetic field which shows a transition from regular to irregular dynamics with increasing field strength in the classical limit. In particular we study the statistical properties of the quasi-spectrum. Our results support the conjecture that Poisson- and GOE-statistics are to be associated with integrable and nonintegrable systems resp. in the semiclassical limit. Approaching the quantum case we observe significant deviations from GOE statistics.     

Intrinsic stochasticity with many degrees of freedom

We study a simple model equation describing a system with an infinity of degrees of freedom which displays an intrinsically chaotic behavior. Some concepts of fully developed turbulence are discussed in relation to this model. We also develop an approach based on Lyapunov exponent measurements. Numerical results on the distribution of Lyapunov numbers and the power spectrum of the associated Lyapunov vectors are presented and briefly discussed.     

Distribution and regulation of stochasticity and plasticity in Saccharomyces cerevisiae

Stochasticity is an inherent feature of complex systems with nanoscale structure. In such systems information is represented by small collections of elements (e.g., a few electrons on a quantum dot), and small variations in the populations of these elements may lead to big uncertainties in the information. Unfortunately, little is known about how to work within this inherently noisy environment to design robust functionality into complex nanoscale systems. Here, we look to the biological cell as an intriguing model system where evolution has mediated the trade-offs between fluctuations and function, and in particular we look at the relationships and trade-offs between stochastic and deterministic responses in the gene expression of budding yeast (Saccharomyces cerevisiae). We find gene regulatory arrangements that control the stochastic and deterministic components of expression, and show that genes that have evolved to respond to stimuli (stress) in the most strongly deterministic way exhibit the most noise in the absence of the stimuli. We show that this relationship is consistent with a bursty two-state model of gene expression, and demonstrate that this regulatory motif generates the most uncertainty in gene expression when there is the greatest uncertainty in the optimal level of gene expression.     

Predator-prey cycles from resonant amplification of demographic stochasticity

We present the simplest individual level model of predator-prey dynamics and show, via direct calculation, that it exhibits cycling behavior. The deterministic analogue of our model, recovered when the number of individuals is infinitely large, is the Volterra system (with density-dependent prey reproduction) which is well known to fail to predict cycles. This difference in behavior can be traced to a resonant amplification of demographic fluctuations which disappears only when the number of individuals is strictly infinite. Our results indicate that additional biological mechanisms, such as predator satiation, may not be necessary to explain observed predator-prey cycles in real (finite) populations.