Coarse and fine grained entropy?

[SW VandeCarr]

I'm confused by coarse and fine grained entropy and how they're related to the standard Boltzmann and Gibbs equations. I understand the Gibbs equation is useful even when a system is not in equilibrium. The linked reference seems to say that fine grained entropy is always (or tends to) zero and coarse grained entropy is always (or tends to)positive infinity. Is this true? If so, does it obviate the standard Boltzmann and Gibbs models? Since practical applications are concerned with changes in entropy, not the absolute values, I must not have correctly understand the article. I'm familiar with Shannon entropy, but not so much with the details of thermodynamic entropy.

http://www.mi.ras.ru/~vvkozlov/fulltext/196_e.pdf

 

[SW VandeCarr]

I'll make my question more specific. In section 2 of the above cited paper "..the absence of approximation" the authors state that coarse grained entropy does not approximate fine grained entropy, in the general case, as the partition is refined (last paragraph of section 2). Is this the prevailing view at the present time?