  We provide a justification, via the thermodynamic limit, of the modular
formula for entropy production in two-times measurement proposed in [Benoist,
Bruneau, Jak\v{s}i\'c, Panati and Pillet: arxiv:2310.10582]. We consider the
cases of open quantum systems in which all thermal reservoirs are either
(discrete) quantum spin systems or free Fermi gases.
