Nonequilibrium Fluctuation Relation for Sheared Micellar Gel in a Jammed State

Abstract

We show that the shear rate at a fixed shear stress in a micellar gel in a jammed state exhibits large fluctuations, showing positive and negative values, with the mean shear rate being positive. The resulting probability distribution functions (PDF's) of the global power flux to the system vary from Gaussian to non-Gaussian, depending on the driving stress and in all cases show similar symmetry properties as predicted by Gallavotti-Cohen steady state fluctuation relation. The fluctuation relation allows us to determine an effective temperature related to the structural constraints of the jammed state. We have measured the stress dependence of the effective temperature. Further, experiments reveal that the effective temperature and the standard deviation of the shear rate fluctuations increase with the decrease of the system size. with Σ = 1. Here, s τ = 1 τ t+τ t s(t ) dt and s(t) is the rate of entropy production in the non-equilibrium steady state. P (+s τ ) is the probability of observing a fluctuation of magnitude s τ over a phase space trajectory of duration τ which is larger than any microscopic time scale of the system. Naturally, P (−s τ ) gives the probability of transient violation of second law of thermodynamics for the time τ , as the entropy decreases over this time.The physical implication of Eq (1) is that, if the value of s τ and τ is large, as in case of macroscopic systems and time scales, P (+s τ ) >> P (−s τ ), i.e. the probability of observing entropy increasing fluctuations are overwhelmingly large compared to those in which entropy decreases. Thus, in classical thermodynamics we never see the decrease in entropy in any physical process. Extension of steady state fluctuation theorem for finite times is discussed in [6]. The experiments on Fluctuation Relation (FR) reported so far can be broadly divided into two classes. Experiments on systems with small number of degrees of freedom include dragging of a Brownian particle in an optical trap [7,8], electrical circuits [9], RNA stretching [10,11] where RNA free energy between folded and unfolded states were estimated using Crook's Relation and Jarzynski Equality and stochastic harmonic oscillators [12,13]. The second class of experiments which is of relevance here, includes macroscopic systems with large number of degrees of freedom such as, Rayleigh-Benard convection [14,15], pressure fluctuations on a surface kept in turbulent flows [4], vertically shaken granular beads [5], Lagrangian turbulence on a free surface [16] and liquid crystal electro-convection [17]. To our knowledge no experimental evidence exists for the FR in large volume sheared fluids. In this Letter we address, for the first time, instance of the FR in case of a macroscopic sized sheared micellar gel in a jammed state. In our context s(t) =, where P(t) is the instantaneous power flux into the system and T ef f is the effective temperature of the system. We show that the nature of PDF's of global power flux for the same system can be Gaussian or non-Gaussian, depending on t...

Negative velocity fluctuations and non-equilibrium fluctuation relation for a driven high critical current vortex state

“…Note that negative velocity fluctuations haven’t been reported earlier close to any conventional vortex depinning regimes 4–14, 20–27 . However, driving a colloidal system out of its jammed state shows unusual negative and positive fluctuations in shear rate 28 which are analogous to the negative and positive vortex velocity fluctuations we observe near .…”

“…GC-NEFR states the probability of power generating events (events associated with particles drifting opposite to drive, or negative velocity events) is exponentially small compared to power consuming events (events associated with particles drifting in the direction of the drive, or positive velocity events). The GC-NEFR has been experimentally verified in various driven systems like, dragged colloidal particles in an optical trap, electrical circuits and jammed state in sheared micellar gel 28, 45–49 . We analyse the non-Gaussian P ( V ) distribution with negative velocity tail near (see Fig.…”

“…At lower I (just above ), the fluctuating state exhibits unusual negative velocity events associated with vortices drifting opposite to the drive direction. In this regime the velocity distribution is non-Gaussian with a significant negative velocity tail and the distribution obeys the Gallavotti-Cohen Non-Equilibrium Fluctuation Relation 28–36 (GC-NEFR). The GC-NEFR analysis provides a measure of an effective energy scale ( E eff ) and we also determine the large deviation function (LDF) associated with these unusual fluctuation events.…”

Large deviation statistics of non-equilibrium fluctuations in a sheared model-fluid

“…The Evans-Searles FT has been verified in a number of molecular dynamics simulations, electrical resistor circuits [8], and for a colloidal particle in an optical trap [6,7]. The Gallavotti-Cohen FT has been satisfied in many real systems such as in turbulent flows [9][10][11], turbulent RayleighBénard convection [12], vertically agitated granular gas [13] and in a sheared micellar gel [14].…”

Work fluctuations for a Brownian particle driven by a correlated external random force

“…The FT expresses universal properties of the probability density function (PDF) p(Ω) for functional Ω[x(τ)], like work, heat, power flux or entropy production, evaluated along the fluctuating trajectories x(τ) taken from ensembles with well-specified initial distributions. There have been a number of theoretical and experimental [27][28][29][30][31][32][33][34][35][36][37] studies to elucidate different aspects of FT. We refer to the recent review [1] which contains an extensive list of references both from the theoretical and the experimental aspects.…”