Two constructive proofs on d-majorization and thermo-majorization
Statistical Mechanics
2020-11-30 v1 Mesoscale and Nanoscale Physics
Quantum Physics
Abstract
Two constructive proofs on d-majorization and thermo-majorization are provided. In the first part, we present a diagrammatic proof of the equivalence between d-majorization and the existence of a proper stochastic matrix. We explicitly construct the desired stochastic matrix by using a graphical argument. In the second part, we present a constructive proof of the equivalence between the Gibbs-preserving map and thermal operation in classical systems. We construct the desired thermal operation and a heat bath which emulates any Gibbs-preserving map with an arbitrary accuracy.
Cite
@article{arxiv.2004.14751,
title = {Two constructive proofs on d-majorization and thermo-majorization},
author = {Naoto Shiraishi},
journal= {arXiv preprint arXiv:2004.14751},
year = {2020}
}
Comments
22 pages, 9 figures