Proper normalization removes nonlocal behavior of canonical-based thermodynamic entropy expressions

Equilibrium, canonical based expressions of entropy are known to exhibit non-local effects that can complicate statistical mechanical formulations and applications. Here, we demonstrate that proper normalization of the underlying probability density functions can remove non-local effects in entropy. Our analysis is carried out through third order in density function expansions and lead to results consistent with macroscopic thermodynamics, as required. In addition, we provide complete expressions for smaller dimensional systems that may not conform to the thermodynamic limit.