Passivity constraints on the relations between transmission, reflection, and absorption eigenvalues

Passivity is a fundamental property of many physical systems, characterizing their inability to generate energy. The authors investigate here passivity constraints on the relations between transmission, reflection, and absorption eigenvalues in linear time-invariant systems. The analysis shows that the set of allowable eigenvalue combinations forms a convex polyhedron. The theory reveals a surprising connection to Horn's inequalities, a fundamental result in matrix theory. It has significant implications for the design and optimization of passive devices in optics, acoustics, and mesoscopic physics.