tyyyyyyppooooossss (thx Konstantin)

src/num_results.tex

@@ -1359,7 +1359,7 @@ theorem can be formulated as
   -\dv{\qrelent{ρ_{\sys}(t)}{ρ_{\sys}(∞)}}{t} \geq 0,
 \end{equation}
 where \(\qrelent{ρ}{σ}=\tr[ρ \log_{2} ρ - ρ \log_{2} σ]\) is the
-quantum relative entropy. The left hand side of \cref{eq:spohn} is
+quantum relative entropy. The left-hand side of \cref{eq:spohn} is
 often called entropy production~\cite{Breuer2002Jun,Binder2018}.
 \begin{figure}[htp]
   \centering

src/thermo.tex

@@ -73,7 +73,7 @@ change over one cycle.
 
 In \cref{sec:operational_thermo} a Gibbs like inequality for an
 arbitrary number of baths is derived as a slight generalization of the
-derivation in \refcite{Kato2016Dec}. The left hand side of this
+derivation in \refcite{Kato2016Dec}. The left-hand side of this
 inequality can be associated with a thermodynamic cost that should be
 minimized for optimal efficiency.
 
@@ -674,7 +674,7 @@ energy that is simply transferred between the baths.
 An argument based on entropy may be made for the periodic steady state
 as was shown in \refcite{Kato2016Dec} and is reproduced here with the
 slight generalization of multiple baths and modulated coupling. We
-will find a Clausius like form of the second law. The left hand side
+will find a Clausius-like form of the second law. The left-hand side
 of this inequality can then be interpreted as thermodynamic cost of
 the cyclical process.
 
@@ -778,7 +778,7 @@ In fact, the requirement that \(ΔE_{\bath^i}^\cyc\) be constant can be
 relaxed, as \cref{eq:secondlaw_cyclic} holds as soon as
 \(ΔS_\sys^\cyc\) vanishes.
 
-The left hand side could be called ``bath entropy production'' as is
+The left-hand side could be called ``bath entropy production'' as is
 motivated in \refcite{Riechers2021Apr}, where heat is identified with
 \(ΔE_{\bath^i}\). There, the entropy production bound
 \cref{eq:bathenergyandsystementro} that takes into account system and
@@ -1311,7 +1311,7 @@ the usefulness and validity of the considerations of
 per cycle and efficiency, as well as the cost measure introduced
 there.
 
-A standard thermodynamic cycle that is a popular model in the
+A standard thermodynamic cycle which is a popular model in the
 literature\footnote{see
   \cite{Wiedmann2021Jun,Karimi2016Nov,Binder2018}} is a quantum heat
 engine inspired by the Otto cycle. Similar to expansion and