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Addendum reports a new proof for the generalized Langevin equation using variation of constants, simplifying previous methods.
Theorem 2.5 gives a proof of the GLE and 2FDT for the Mori projection. We note that the same result is obtained by a variation of constants, which greatly simplifies the semigroup approach presented in section 2. We therefore add a short proof of the GLE by means of the variation of constants formula for strongly continuous semigroups.
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Widder et al. (2026) studied this question.
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