Erratum: About the foundation of the Kubo generalized cumulants theory: A revisited and corrected approach (Journal of Statistical Mechanics: Theory and Experiment (2020) 4 (043405) DOI: 10.1088/1742-5468/ab7755)

Page 13: after equation (34): Erratum: then M⁽A⁾ and M⁽B⁾ are M-unconnected to each vector spaces. Corrected: then M⁽A⁾ and M⁽B⁾ are vector spaces M-unconnected to each other. Page 14: Definition M contains different typos. It should be replaced with the following one: Definition M. If Ω₁ and Ω₂ are two random q-numbers with generalized moment generating functions M₁:= (exp_M[Ω₁]) and M₂:= (exp_M[Ω₂]), respectively, then Ω₁ and Ω₂ are defined statistically independent to each other if and only if the generalized moment generating function M₁₊₂:= (exp_M[Ω₁ + Ω₂]) of the random q-number Ω₁ + Ω₂ is given by M₁ * M₂. Page 16: two lines before equation (45): Erratum: In practice, exploiting equations (36), (37) and (44) says that Correction: In practice, exploiting equations (36) and (37), equation (44) says that Page 18: in lemma 2: Erratum: exp_MO [K(T)] exp_MO [K(T)] = exp_MO [K(T) + K(T)]. Correction: exp_MO [K(T)] * exp_MO [K(T)] = exp_MO [K(T) + K(T)].