Chemical potential: Gibbs-Duhem approach

The most commonly used method of calculating the chemical potential in quantum statistical mechanics is based on an idea originally due to Sommerfeld, applicable to a Fermi system. An alternative approach is presented that relies on the extensivity property of the energy on an isentrope. A simple equivalence is demonstrated through the ideal gas models given in the polylogarithm formulation. Unlike the Sommerfeld approach this approach is also applicable to a Bose system.