Erratum: "Evolution equations for open systems and collective variables: Which equation would you like to solve by molecular dynamics simulation?" [J. Chem. Phys. 161, 191501 (2024)].

The article addresses a correction to a previous tutorial on the generalized Langevin equation (GLE), specifically regarding a misplaced and inaccurate remark about the conditions required for applying the Dyson identity in deriving the GLE. The original remark incorrectly linked certain mathematical conditions—such as square integrability of observables and positivity of phase space densities—to the strong continuity of the orthogonal dynamics semigroup, a property necessary for the Dyson identity. This assumption was based on an unpublished thesis later found to contain errors. Recent clarifications have refined the precise conditions under which the Dyson identity holds, though these are mathematically complex and not detailed here. The main results involving the Mori projection operator remain valid, but caution is advised for the section using the Zwanzig projection operator, as it is currently unclear if the Dyson identity applies in that context.