  We investigate thermal one-loop effective potentials in multi-flavor models
with chemical potentials. We study four-dimensional models in which each flavor
have different global U(1) charges. Accordingly they have different chemical
potentials. We call these "non-uniform chemical potentials," which are
organized into a diagonal matrix \mu. The mass matrix at a vacuum does not
commute with \mu. We find that the effective potential is divided into three
parts. The first part is the Coleman-Weinberg potential. The UV divergence
resides only in this part. The second is the correction to the Coleman-Weinberg
potential that is independent of temperature, and the third depends on both
temperature and \mu. Our result is a generalization of the thermal potentials
in previous studies for models with single and multi-flavors with (uniform)
chemical potentials and reproduces all the known results correctly.
