@BjornLomborg Foolish foreign policy by G. Schroeder and A. Merkel lead to this. They were warned many times by Poland and Baltic states. Once again German ignorance and arrogance makes Europe suffer. O. Scholz in no better.
@johncarlosbaez S for quantum harmonic oscillator is (ℏω/2T)Coth(ℏω/2T) + k ln[Csch(ℏω/2T)] (sum Exp[(n+1/2)ℏω/2T] to get Z, then S). In the classical limit k T >>> ℏω you get your result. The additional 1 comes from Coth() part which is from the n=0 mode so it is a quantum effect (nice!).