On dissipation in crackling noise systems

Laboratoire de Physico-Chimie Théorique, CNRS UMR Gulliver 7083, PSL Research University, ESPCI 10 rue de Vauquelin, 75231 Paris cedex 05, France and PMMH, CNRS UMR 7636, PSL Research University, ESPCI - 10 rue de Vauquelin, 75231 Paris cedex 05, France

^(a) reinaldomeister@gmail.com

Received: 2 January 2018
Accepted: 28 February 2018

Abstract

We consider the amount of energy dissipated during individual avalanches at the depinning transition of disordered and athermal elastic systems. Analytical progress is possible in the case of the Alessandro-Beatrice-Bertotti-Montorsi (ABBM) model for Barkhausen noise, due to an exact mapping between the energy released in an avalanche and the area below a Brownian path until its first zero-crossing. Scaling arguments and examination of an extended mean-field model with internal structure show that dissipation relates to a critical exponent recently found in a study of the rounding of the depinning transition in the presence of activated dynamics. A new numerical method to compute the dynamic exponent at depinning in terms of blocked and marginally stable configurations is proposed, and a kind of “dissipative anomaly” —with potentially important consequences for non-equilibrium statistical mechanics— is discussed. We conclude that for depinning systems the size of an avalanche does not constitute by itself a univocal measure of the energy dissipated.