  The importance of mesoscale fluctuations in flowing amorphous materials is
widely accepted, without a clear understanding of their role. We propose a
mean-field elastoplastic model that admits both stress and strain-rate
fluctuations, and investigate the character of its power distribution under
steady shear flow. The model predicts the suppression of negative power
fluctuations near the liquid-solid transition; the existence of a fluctuation
relation in limiting regimes but its replacement in general by
stretched-exponential power-distribution tails; and a crossover between two
distinct mechanisms for negative power fluctuations in the liquid and the
yielding solid phases. We connect these predictions with recent results from
particle-based, numerical micro-rheological experiments.
