On dissipation in crackling noise systems

TL;DR

This paper investigates energy dissipation during avalanches at the depinning transition in disordered elastic systems, revealing a connection to critical exponents and proposing new computational methods and theoretical insights.

Contribution

It provides an exact analytical mapping for ABBM model, introduces a novel numerical method for dynamic exponent calculation, and discusses the implications of dissipation in depinning systems.

Findings

Dissipation relates to a critical exponent in depinning transitions.

Avalanche size alone does not measure energy dissipation.

A new numerical method for dynamic exponent computation is proposed.

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 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 nonequilibrium 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.