Population Capacity and the Geometry of Thermomajorization
Abstract
We characterize quasiclassical state conversion under thermal operations through population capacities: the maximum population that thermal operations can concentrate on each set of energy levels. These capacities form a normalized, nondecreasing submodular rank function whose base polytope is exactly the thermally reachable population region. Their bounds therefore provide a complete system of accessibility constraints. Every nested chain of capacities can be simultaneously saturated by a reachable state, yielding the maximum expectation value of any prescribed observable, including the system Hamiltonian. For a prescribed target, its thermomajorization prefixes suffice to certify exact conversion through at most n−1 binary work-extraction probes. For approximate conversion, we construct a distinguished reachable state from active capacity constraints using a weighted principal sequence in O(n2 log n) operations. At fixed comparison weights, this state minimizes every weighted convex separable residual cost and realizes a common first contact with the corresponding target-centered smoothing regions. Finally, the optimal trace-distance error equals the largest capacity advantage of the target over the initial state. This gap is attained at a target prefix and equals the largest positive optimized energy-storage deficit among the same binary probes, divided by their energy gap. Thus a common population capacity geometry determines accessibility, observable optimization, conversion certificates, and universal approximation.
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BibTeX
@misc{meroi2026population,
title = {{Population Capacity and the Geometry of Thermomajorization}},
author = {F. Meroi and C. Massri and M. Losada and G. Bellomo and G. M. Bosyk},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35433},
eprint = {2610.35433},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35433},
}
RIS
TY - UNPB
TI - Population Capacity and the Geometry of Thermomajorization
AU - F. Meroi
AU - C. Massri
AU - M. Losada
AU - G. Bellomo
AU - G. M. Bosyk
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35433
UR - https://arxiv.org/abs/2610.35433
AB - We characterize quasiclassical state conversion under thermal operations through population capacities: the maximum population that thermal operations can concentrate on each set of energy levels. These capacities form a normalized, nondecreasing submodular rank function whose base polytope is exactly the thermally reachable population region. Their bounds therefore provide a complete system of accessibility constraints. Every nested chain of capacities can be simultaneously saturated by a reachable state, yielding the maximum expectation value of any prescribed observable, including the system Hamiltonian. For a prescribed target, its thermomajorization prefixes suffice to certify exact conversion through at most n−1 binary work-extraction probes. For approximate conversion, we construct a distinguished reachable state from active capacity constraints using a weighted principal sequence in O(n^2 log n) operations. At fixed comparison weights, this state minimizes every weighted convex separable residual cost and realizes a common first contact with the corresponding target-centered smoothing regions. Finally, the optimal trace-distance error equals the largest capacity advantage of the target over the initial state. This gap is attained at a target prefix and equals the largest positive optimized energy-storage deficit among the same binary probes, divided by their energy gap. Thus a common population capacity geometry determines accessibility, observable optimization, conversion certificates, and universal approximation.
ER -