Nonequilibrium fluctuations in a frictional granular motor: Experiments and kinetic theory

Abstract

We report the study of an experimental granular Brownian motor, inspired by the one published in Eshuis et al. [Phys. Rev. Lett. 104, 248001 (2010)], but different in some ingredients. As in that previous work, the motor is constituted by a rotating blade, the surfaces of which break the rotation-inversion symmetry through alternated patches of different inelasticity, immersed in a gas of granular particles. The main difference of our experimental setup is in the orientation of the main axis, which is parallel to the (vertical) direction of shaking of the granular fluid, guaranteeing an isotropic distribution for the velocities of colliding grains, characterized by a variance v(0)(2). We also keep the granular system diluted, in order to compare with Boltzmann-equation-based kinetic theory. In agreement with theory, we observe the crucial role of Coulomb friction which induces two main regimes: (i) rare collisions, with an average angular velocity <ω>~v(0)(3), and (ii) frequent collisions (FC), with <ω>~v(0). We also study the fluctuations of the angle spanned in a large-time interval Δθ, which in the FC regime is proportional to the work done upon the motor. We observe that the fluctuation relation is satisfied with a slope which weakly depends on the relative collision frequency.

Asymptotic Derivation of Langevin-like Equation with Non-Gaussian Noise and Its Analytical Solution

“…We here explain an asymptotic connection from the non-Gaussian Langevin equation (23) to the Gaussian one (34) in terms of the amplitude of the frictional effect. We first make the assumptions (i), (iv'), the linear friction A ε (v) = γ εv , and the symmetric jump noise W (0; Y) = W (0; −Y) (or equivalently, K * 2n+1;(0) = 0), and restrict our analysis to the following two cases: 1.…”

“…Non-linear frictions are ubiquitous in nature [55][56][57] and are known to appear in systems such as granular [58][59][60], biological [61][62][63][64] and atomic-surface ones [65][66][67]. We note that non-linear frictions can be discontinuous functions with respect to velocity in general (e.g., Coulombic friction), and their singular effects on stochastic properties have been interesting topics [31][32][33][34]51,[68][69][70][71][72][73][74][75][76][77]. Indeed, as will be shown in the next section, the distribution function can be strongly singular around the peak.…”

“…For example, athermal noise (e.g., avalanche [28,29] or shot noise [30]) plays an important role as well as thermal noise in electrical circuits. In granular and biological systems, it is known that the granular noise [31][32][33][34] and active noise [35,36], respectively, appear because of external vibration and consumption of adenosine triphosphate (ATP). These systems cannot be addressed by the conventional microscopic theories because they are coupled with multiple environments.…”

Heat fluctuations of Brownian oscillators in nonstationary processes: Fluctuation theorem and condensation transition

“…A major advance in this direction has been made in the last two decades with the development of Fluctuations Theorems (FT), which allow to constrain the form of the distributions with a certain degree of universality and in conditions arbitrarily far from equilibrium [1]. This theoretical approach turned out to be very useful, both in experimental and numerical studies, in the characterization of several nonequilibrium systems, such as colloidal particles in harmonic traps [2][3][4][5], vibrated granular media [6][7][8], models of coupled Langevin equations [9][10][11], driven stochastic Lorentz gases [12,13], and active matter [14], just to name a few examples.…”

Coulomb Friction Driving Brownian Motors

“…A finite drift could be achieved in the case of inelastic collisions, which has been considered elsewhere [3,26].…”