An analogue of the classical link between the relative entropy and Fisher information entropy is presented in the context of free probability theory. Several generalizations of the relative entropy in terms of density matrices are also discussed.
BELL, H. E., & KLEIN, A. A. (1999). NONCOMMUTATIVITY AND NONCENTRAL ZERO DIVISORS. International Journal of Mathematics and Mathematical Sciences, 1999(), 67-74. https://doi.org/10.1155/S0161171299220674
SlDDIQI, A., & ANSARI, Q. (1993). ON THE NONLINEAR IMPLICIT COMPLEMENTARITY PROBLEM. International Journal of Mathematics and Mathematical Sciences, 1993(), 783-789. https://doi.org/10.1155/S0161171293000973