  Understanding the entropy production of systems strongly coupled to thermal
baths is a core problem of both quantum thermodynamics and mesoscopic physics.
While there exist many techniques to accurately study entropy production in
such systems, they typically require a microscopic description of the baths,
which can become numerically intractable to study for large systems.
Alternatively an open-systems approach can be employed with all the nuances
associated with various levels of approximation. Recently, the mesoscopic leads
approach has emerged as a powerful method for studying such quantum systems
strongly coupled to multiple thermal baths. In this method, a set of
discretised lead modes, each locally damped, provide a Markovian embedding.
Here we show that this method proves extremely useful to describe entropy
production of a strongly coupled open quantum system. We show numerically, for
both non-interacting and interacting setups, that a system coupled to a single
bath exhibits a thermal fixed point at the level of the embedding. This allows
us to use various results from the thermodynamics of quantum dynamical
semi-groups to infer the non-equilibrium thermodynamics of the strongly
coupled, non-Markovian central systems. In particular, we show that the entropy
production in the transient regime recovers the well established microscopic
definitions of entropy production with a correction that can be computed
explicitly for both the single- and multiple-lead cases.
