We use the Falcone–Takesaki non-commutative flow of weights and the resulting theory of non-commutative Lp spaces in order to define the family of relative entropy functionals that naturally generalise the quantum relative entropies of Jenčová– Ojima and the classical relative entropies of Zhu–Rohwer, and belong to an intersection of families of Petz relative entropies with Bregman relative ent...