In quantum mechanics to each observable is associated a matrix. If the system is generic -- no special symmetries -- one expects a certain degree of randomness for the elements of these matrices. This has been encoded in the "Eigenstate Thermalization Hypothesis" (ETH), proposed some thirty years ago. However, the formulation of ETH needed to be completed, taking into account correlations that had been neglected. Once this is done, the formulation becomes quite complicated -- but it turns out that Free Probability comes to the rescue.
