Statistical and Classical Entropy

Contrary to what happens for mechanical systems, chemical systems do not reach equilibrium by minimizing their internal energy. The essential difference is that in 

Further manipulations give the Boltzmann equilibrium distribution and the total entropy of an ideal gas  

The partition function (2 has a translational, rotational and vibrational part, and so does entropy. The first two contributions can be calculated in a straightforward way, but the vibrational contribution to entropy requires a knowledge of the normal vibrational frequencies of the molecule or of the crystal. 

The classical definition of entropy goes through the Clausius inequality  

---