Thanks for you answer. I agree with you but I'm still a little bit confused by Reichls statement. However, I would also agree with that if the following is true (closed system, no chemical reactions, Volume work being the only work interaction coordinate).
\begin{align*}
dU &= dQ + dW ~~~(1) \\...
As far as I learned, the following statements should be correct (for closed systems, no chemical reactions), irrespective whether the process is reversible or irreversible (since S and V are state variables):
dU=TdS−pdV
dU=dQ+dW
Does this imply, that the statement:
dU≤TdS−pdV
is wrong?
This...