PreprintarXiv licencearXiv
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.
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BibTeX
@misc{holm2026maximum,
title = {{Maximum entropy explanation for the ubiquity of power-law mechanical responses}},
author = {Sverre Holm},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03999},
eprint = {2611.03999},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03999},
}
RIS
TY - UNPB
TI - Maximum entropy explanation for the ubiquity of power-law mechanical responses
AU - Sverre Holm
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03999
UR - https://arxiv.org/abs/2611.03999
AB - 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.
ER -