Scaling, fractal, and Hurst effects in spontaneous violations of entropy inequality in granular Couette systems

Abstract

Planar Couette flows of granular systems are investigated at different spatial and time scales using computational dynamics to determine their stochastic characteristics. Systems with one or two sizes of circular disks with frictional-Hookean contacts are studied. While spontaneous violations of the second law of thermodynamics always follow the fluctuation theorem, time and spatial dependencies of the dissipation as a random process are determined for multiple regimes. Given that grain rotations are degrees of freedom separate from grain translations, the dissipation is calculated from a micropolar model. In monosized disk systems, it is found that the dissipation is Gaussian and, for successively smaller systems, it tends to have a skewed Cauchy probability distribution. Multi-diameter grain flows, once a steady-state mixture of the particles occurs, are comparable to the average diameter monosized granular flow. The flows' dissipation is found to be very closely modeled by a random process with the Cauchy covariance function, whose numerical parameters imply fractal and anti-persistent long-memory characters.