Finite sampling effects on generalized fluctuation-dissipation relations for steady states

We study the effects of the finite number of experimental data on the computation of a generalized fluctuation-dissipation relation around a nonequilibrium steady state of a Brownian particle in a toroidal optical trap. We show that the finite sampling has two different effects, which can give rise to a poor estimate of the linear response function. The first concerns the accessibility of the generalized fluctuation-dissipation relation due to the finite number of actual perturbations imposed to the control parameter. The second concerns the propagation of the error made at the initial sampling of the external perturbation of the system. This can be highly enhanced by introducing an estimator which corrects the error of the initial sampled condition. When these two effects are taken into account in the data analysis, the generalized fluctuation-dissipation relation is verified experimentally

The Hatano-Sasa equality: transitions between steady states in a granular gas

An experimental study is presented, about transitions between Non-Equilibrium Steady States (NESS) in a dissipative medium. The core device is a small rotating blade that imposes cycles of increasing and decreasing forcings to a granular gas, shaken independently. The velocity of this blade is measured, subject to the transitions imposed by the periodic torque variation. The Hatano-Sasa equality, that generalises the second principle of thermodynamics to NESS, is verified with a high accuracy (a few $10^{-3}$), at different variation rates. Besides, it is observed that the fluctuating velocity at fixed forcing follows a generalised Gumbel distribution. A rough evaluation of the mean free path in the granular gas suggests that it might be a correlated system, at least partially

Coarsening in potential and nonpotential models of oblique stripe patterns

We study the coarsening of two-dimensional oblique stripe patterns by numerically solving potential and nonpotential anisotropic Swift-Hohenberg equations. Close to onset, all models exhibit isotropic coarsening with a single characteristic length scale growing in time as $t^{1/2}$. Further from onset, the characteristic lengths along the preferred directions $\hat{x}$ and $\hat{y}$ grow with different exponents, close to 1/3 and 1/2, respectively. In this regime, one-dimensional dynamical scaling relations hold. We draw an analogy between this problem and Model A in a stationary, modulated external field. For deep quenches, nonpotential effects produce a complicated dislocation dynamics that can lead to either arrested or faster-than-power-law growth, depending on the model considered. In the arrested case, small isolated domains shrink down to a finite size and fail to disappear. A comparison with available experimental results of electroconvection in nematics is presented.Comment: 13 pages, 13 figures. To appear in Phys. Rev.

Steady state fluctuation relations for systems driven by an external random force

We experimentally study the fluctuations of the work done by an external Gaussian random force on two different stochastic systems coupled to a thermal bath: a colloidal particle in an optical trap and an atomic force microscopy cantilever. We determine the corresponding probability density functions for different random forcing amplitudes ranging from a small fraction to several times the amplitude of the thermal noise. In both systems for sufficiently weak forcing amplitudes the work fluctuations satisfy the usual steady state fluctuation theorem. As the forcing amplitude drives the system far from equilibrium, deviations of the fluctuation theorem increase monotonically. The deviations can be recasted to a single master curve which only depends on the kind of stochastic external force.Comment: 6 pages, submitted to EP

Large deviations of heat flow in harmonic chains

We consider heat transport across a harmonic chain connected at its two ends to white-noise Langevin reservoirs at different temperatures. In the steady state of this system the heat $Q$ flowing from one reservoir into the system in a finite time $\tau$ has a distribution $P(Q,\tau)$. We study the large time form of the corresponding moment generating function $\sim g(\lambda) e^{\tau\mu (\lambda)}$. Exact formal expressions, in terms of phonon Green's functions, are obtained for both $\mu(\lambda)$ and also the lowest order correction $g(\lambda)$. We point out that, in general a knowledge of both $\mu(\lambda)$ and $g(\lambda)$ is required for finding the large deviation function associated with $P(Q,\tau)$. The function $\mu(\lambda)$ is known to be the largest eigenvector of an appropriate Fokker-Planck type operator and our method also gives the corresponding eigenvector exactly.Comment: 15 pages; minor modification

Efficiency of Free Energy Transduction in Autonomous Systems

We consider the thermodynamics of chemical coupling from the viewpoint of free energy transduction efficiency. In contrast to an external parameter-driven stochastic energetics setup, the dynamic change of the equilibrium distribution induced by chemical coupling, adopted, for example, in biological systems, is inevitably an autonomous process. We found that the efficiency is bounded by the ratio between the non-symmetric and the symmetrized Kullback-Leibler distance, which is significantly lower than unity. Consequences of this low efficiency are demonstrated in the simple two-state case, which serves as an important minimal model for studying the energetics of biomolecules.Comment: 4 pages, 4 figure

The fluctuation-dissipation relation: how does one compare correlation functions and responses?

We discuss the well known Einstein and the Kubo Fluctuation Dissipation Relations (FDRs) in the wider framework of a generalized FDR for systems with a stationary probability distribution. A multi-variate linear Langevin model, which includes dynamics with memory, is used as a treatable example to show how the usual relations are recovered only in particular cases. This study brings to the fore the ambiguities of a check of the FDR done without knowing the significant degrees of freedom and their coupling. An analogous scenario emerges in the dynamics of diluted shaken granular media. There, the correlation between position and velocity of particles, due to spatial inhomogeneities, induces violation of usual FDRs. The search for the appropriate correlation function which could restore the FDR, can be more insightful than a definition of ``non-equilibrium'' or ``effective temperatures''.Comment: 22 pages, 9 figure

Mode coupling in a hanging-fiber AFM used as a rheological probe

We analyze the advantages and drawbacks of a method which measures the viscosity of liquids at microscales, using a thin glass fiber fixed on the tip of a cantilever of an ultra-low-noise Atomic Force Microscope (AFM). When the fiber is dipped into a liquid, the dissipation of the cantilever-fiber system, which is linked to the liquid viscosity, can be computed from the power spectral density of the thermal fluctuations of the cantilever deflection. The high sensitivity of the AFM allows us to show the existence and to develop a model of the coupling between the dynamics of the fiber and that of the cantilever. This model, which accurately fits the experimental data, gives also more insights into the dynamics of coupled microdevices in a viscous environment. Copyright (C) EPLA, 201

Heat release by controlled continuous-time Markov jump processes

We derive the equations governing the protocols minimizing the heat released by a continuous-time Markov jump process on a one-dimensional countable state space during a transition between assigned initial and final probability distributions in a finite time horizon. In particular, we identify the hypotheses on the transition rates under which the optimal control strategy and the probability distribution of the Markov jump problem obey a system of differential equations of Hamilton-Bellman-Jacobi-type. As the state-space mesh tends to zero, these equations converge to those satisfied by the diffusion process minimizing the heat released in the Langevin formulation of the same problem. We also show that in full analogy with the continuum case, heat minimization is equivalent to entropy production minimization. Thus, our results may be interpreted as a refined version of the second law of thermodynamics.Comment: final version, section 2.1 revised, 26 pages, 3 figure