some small additions

src/thermo.tex

@@ -655,6 +655,11 @@ becomes negligible in the case \(N\gg 1\).
     and becomes more non-monotonous, but never surpasses the bounds.}
 \end{figure}
 
+The important message to take away is, that the ergotropy of the model
+in this section is indeed finite, both for vanishing energy level
+spacing and increasing number of degrees of freedom. We can expect the
+bound \cref{eq:thermo_ergo_bound} to hold in this case with good
+confidence.
 
 After validating the bound of \cref{sec:ergoonebath} for a concrete
 example, we now return to a more generic setting in
@@ -1522,15 +1527,15 @@ remarks in \cref{cha:concl-ideas-future} about \cite{Uzdin2015Sep}.
 \section{Conclusion}
 \label{sec:conclusion-2}
 
-We have reviewed the notion of unitarily extractable energy
-``ergotropy'' and found that this quantity is indeed bounded by
-\cref{eq:thermo_ergo_bound} for the models we study in this work,
-namely finite dimensional systems coupled to a heat bath. It was
+We have reviewed the notion of unitarily extractable energy,
+``ergotropy'', and found that this quantity is indeed bounded by
+\cref{eq:thermo_ergo_bound} for a class of models we studied in this
+work, namely finite dimensional systems coupled to a heat bath. It was
 further demonstrated with an analytical calculation that this bound
-can apply to baths with infinite degrees of freedom. In the
-case of multiple baths, a Gibbs like inequality
-\cref{eq:secondlaw_cyclic} was presented which can be interpreted as
-thermodynamic cost of a cyclical process.
+can apply to baths with infinite degrees of freedom. In the case of
+multiple baths, a Gibbs like inequality \cref{eq:secondlaw_cyclic} was
+presented which can be interpreted as thermodynamic cost of a cyclical
+process.
 
 Subsequently, we studied a modulated version of the spin-boson model
 with the goal of extracting energy from a thermal bath. We found that