Two constructive proofs on d -majorization and thermo-majorization
Naoto Shiraishi · Journal of Physics A Mathematical and Theoretical · 2020
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 arbitrary accuracy.