From equation (36 ) we have

 

The Gibbs entropy equation thus relates the entropy to the probability of occurrence of the possible states of the system. It can be clearly seen that the entropy increases with the number of possible states. For e.g putting p as unity we have S=0, similarly for p=2 we have S=0.693k and for  p=3 we have  S=1.093k .

So from equation 37 we have

 

For other thermodynamic properties we will use the definition i.e

 

From classical thermodynamics we have the equivalent relations i.e