摘要：

The definition of the fundamental quantity, the chemical potential, is badly confused in the
literature: there are at least three distinct definitions in various books and papers. While they
all give the same result in the thermodynamic limit, major differences between them can occur
for finite systems, in anomalous cases even for finite systems as large as a cm3. We resolve
the situation by arguing that the chemical potential defined as the symbol μ conventionally
appearing in the grand canonical density operator is the uniquely correct definition valid for all
finite systems, the grand canonical ensemble being the only one of the various ensembles usually
discussed (microcanonical, canonical, Gibbs, grand canonical) that is appropriate for statistical
thermodynamics, whenever the chemical potential is physically relevant. The zero-temperature
limit of this μ was derived by Perdew et al. for finite systems involving electrons, generally
allowing for electron-electron interactions; we extend this derivation and, for semiconductors, we
also consider the zero-T limit taken after the thermodynamic limit. The enormous finite size
corrections (in macroscopic samples, e.g. 1 cm3) for one rather common definition of the c.p.,
found recently by Shegelski within the standard effective mass model of an ideal intrinsic semiconductor,
are discussed. Also, two very-small-system examples are given, including a quantum dot.