Noether Symmetries Generate Deterministic Energy-Harvesting Protocols
Abstract
We consider the general principles for when deterministic energy harvesting (DEH) is possible. DEH means absorbing energy from a fluctuating source without entropy being absorbed. We show that the symmetry structure of the source--harvester dynamics gives a general route beyond existing examples to identify DEH capable source states. Any continuous symmetry with a conserved Noether charge induces a source-side orbit of states that all implement the same deterministic harvester transition, provided the harvester boundary states are symmetry invariant. Consequently, one DEH capable source state with nonzero asymmetry between charge sectors can generate infinitely many simultaneously DEH capable source states. A Jaynes-Cummings model, a three-spin XX chain, and an SU(2) model illustrate the construction. We further extend Noether's theorem to generalised probabilistic theories and thereby generalise our main result. We further establish an asymmetry bound for harvesting, showing that source asymmetry cannot increase on average, while DEH saturates the bound exactly preserving asymmetry.
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BibTeX
@misc{akil2026noether,
title = {{Noether Symmetries Generate Deterministic Energy-Harvesting Protocols}},
author = {Ali Akil and M. Hamed Mohammady and Zihan Wang and Oscar Dahlsten},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10533},
eprint = {2609.10533},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10533},
note = {CC0},
}
RIS
TY - UNPB
TI - Noether Symmetries Generate Deterministic Energy-Harvesting Protocols
AU - Ali Akil
AU - M. Hamed Mohammady
AU - Zihan Wang
AU - Oscar Dahlsten
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10533
UR - https://arxiv.org/abs/2609.10533
AB - We consider the general principles for when deterministic energy harvesting (DEH) is possible. DEH means absorbing energy from a fluctuating source without entropy being absorbed. We show that the symmetry structure of the source--harvester dynamics gives a general route beyond existing examples to identify DEH capable source states. Any continuous symmetry with a conserved Noether charge induces a source-side orbit of states that all implement the same deterministic harvester transition, provided the harvester boundary states are symmetry invariant. Consequently, one DEH capable source state with nonzero asymmetry between charge sectors can generate infinitely many simultaneously DEH capable source states. A Jaynes-Cummings model, a three-spin XX chain, and an SU(2) model illustrate the construction. We further extend Noether's theorem to generalised probabilistic theories and thereby generalise our main result. We further establish an asymmetry bound for harvesting, showing that source asymmetry cannot increase on average, while DEH saturates the bound exactly preserving asymmetry.
ER -