Maximum entropy explanation for the ubiquity of power-law mechanical responses

Abstract

The ubiquitous power-law relaxation emerges from complex mechanical systems with a vast number of interacting exponential responses. Here we demonstrate that power-law responses satisfy a maximum entropy criterion, regulating the individual contributions under partial knowledge. This leads to a prediction that frequency range of validity decreases with power-law exponent, a property which is confirmed for some biological materials. The close relation with the fractional standard linear solid also leads to an incorporation of the equally ubiquitous stretched exponential behavior.