Ergotropy from energetic coherence and the third law of thermodynamics
Abstract
We study the ergotropy and the thermodynamic potentials of a qubit battery charged by repeated interactions with clusters of thermal ancillas, qubits or oscillators, through a composite system-bath coupling that generates steady-state coherence in the energy basis. A single parameter encoding the bath quantum statistics yields the coherence and ergotropy in closed form for any cluster size. For large clusters, the ergotropy becomes independent of the bath statistics and, at optimal couplings, reaches a universal fraction of the equilibrium internal energy of the qubit at the bath temperature. Since the charged state has no population inversion, all extractable work comes from coherence. The ergotropy is flat at low temperatures. We trace this plateau to the third law, and show that the ergotropy is proportional to the equilibrium enthalpy of the qubit, whose slope vanishes with the heat capacity. For a battery composed of multiple qubits, the coherence grows exponentially with the number of qubits while the ergotropy grows linearly, both remaining a nearly constant fraction of their respective maxima. The charged state is a non-equilibrium steady state with finite entropy at zero temperature, sustained by the work of switching the collisional interaction on and off. The cost is nonzero whenever the parallel coupling is nonzero, and, unlike the ergotropy, it depends on the bath statistics.
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BibTeX
@misc{yanezsoria2026ergotropy,
title = {{Ergotropy from energetic coherence and the third law of thermodynamics}},
author = {O. S. Yáñez-Soria and G. Guarnieri and B. Çakmak and R. Román-Ancheyta},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38724},
eprint = {2609.38724},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38724},
}
RIS
TY - UNPB
TI - Ergotropy from energetic coherence and the third law of thermodynamics
AU - O. S. Yáñez-Soria
AU - G. Guarnieri
AU - B. Çakmak
AU - R. Román-Ancheyta
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.38724
UR - https://arxiv.org/abs/2609.38724
AB - We study the ergotropy and the thermodynamic potentials of a qubit battery charged by repeated interactions with clusters of thermal ancillas, qubits or oscillators, through a composite system-bath coupling that generates steady-state coherence in the energy basis. A single parameter encoding the bath quantum statistics yields the coherence and ergotropy in closed form for any cluster size. For large clusters, the ergotropy becomes independent of the bath statistics and, at optimal couplings, reaches a universal fraction of the equilibrium internal energy of the qubit at the bath temperature. Since the charged state has no population inversion, all extractable work comes from coherence. The ergotropy is flat at low temperatures. We trace this plateau to the third law, and show that the ergotropy is proportional to the equilibrium enthalpy of the qubit, whose slope vanishes with the heat capacity. For a battery composed of multiple qubits, the coherence grows exponentially with the number of qubits while the ergotropy grows linearly, both remaining a nearly constant fraction of their respective maxima. The charged state is a non-equilibrium steady state with finite entropy at zero temperature, sustained by the work of switching the collisional interaction on and off. The cost is nonzero whenever the parallel coupling is nonzero, and, unlike the ergotropy, it depends on the bath statistics.
ER -