  We study the energy shift and the Casimir-Polder force of an atom out of
thermal equilibrium near the surface of a dielectric substrate. We first
generalize, adopting the local source hypothesis, the formalism proposed by
Dalibard, Dupont-Roc and Cohen-Tannoudji, which separates the contributions of
thermal fluctuations and radiation reaction to the energy shift and allows a
distinct treatment to atoms in the ground and excited states, to the case out
of thermal equilibrium, and then use the generalized formalism to calculate the
energy shift and the Casimir-Polder force of an isotropically polarizable
neutral atom. We identify the effects of the thermal fluctuations that
originate from the substrate and the environment and discuss in detail how the
Casimir-Polder force out of thermal equilibrium behaves in three different
distance regions in both the low-temperature limit and the high-temperature
limit for both the ground-state and excited-state atoms, with special attention
devoted to the new features as opposed to thermal equilibrium. In particular,
we recover the new behavior of the atom-wall force out of thermal equilibrium
at large distances in the low temperature limit recently found in a different
theoretical framework and furthermore we give a concrete region where this
behavior holds.
