This paper considers a class of entropy functionals defined for random matrices, and it demonstrates that these functionals satisfy a subadditivity property. Several matrix concentration inequalities are derived as an application of this result.
Joel Tropp. Richard Chen. "Subadditivity of matrix $\varphi$-entropy and concentration of random matrices." Electron. J. Probab. 19 1 - 30, 2014. https://doi.org/10.1214/EJP.v19-2964