Shannon and Statistical Entropies

In Chap.  2 , we saw that the thermodynamic variables are expressible in terms of various partial derivatives of entropy. The link between mechanical and thermodynamic descriptions may therefore be established by identifying suitably defined mechanical entropy, i.e. entropy defined in terms of mechanical variables with thermodynamic entropy. In Chap.  4 , we saw that identification of Boltzmann entropy with thermodynamic entropy provides the desired link when particles are non-interacting. We will see that entropy for systems of N interacting particles, identifiable with thermodynamic entropy, is Gibbs entropy [1] defined in terms of N-particle phase space distribution function. The Boltzmann entropy for the gas of N molecules on the other hand is in terms of single-particle distribution function. It does not depend on inter-particle interaction even when inter-particle interaction is present and does not correspond to thermodynamic entropy in the presence of inter-particle interaction [2].