  We investigate the quantum field aspects in flat spacetime for an uniformly
accelerated observer moving in a thermal bath. In particular, we obtain an
exact closed expression of the reduced density matrix for an uniformly
accelerated observer with acceleration $a = 2\pi T$ when the state of the
quantum field is a thermal bath at temperature $T^\prime$. We find that the
density matrix has a simple form with an effective partition function $Z$ being
a product, $Z = Z_T Z_{T^\prime}$, of two thermal partition functions
corresponding to temperatures $T$ and $T^\prime$ and hence is not thermal, even
when $T = T^\prime$. We show that, even though the partition function has a
product structure, the two thermal baths are, in fact, interacting systems;
although in the high frequency limit $\omega_k \gg T$ and $\omega_k \gg
T^\prime$, the interactions are found to become sub-dominant. We further
demonstrate that the resulting spectrum of the Rindler particles can be
interpreted in terms of spontaneous and stimulated emission due to the
background thermal bath. The density matrix is also found to be symmetric in
the acceleration temperature $T$ and the thermal bath temperature $T^\prime$
indicating that thermodynamic experiments alone cannot distinguish between the
thermal effects due to $T$ and those due to $T^\prime$. The entanglement
entropy associated with the reduced density matrix (with the background
contribution of the Davies-Unruh bath removed) is shown to satisfy, in the
$\omega_k \gg T^\prime$ limit, a first law of thermodynamics relation of the
form $T \delta S = \delta E$ where $\delta E$ is the difference in the energies
corresponding to the reduced density matrix and the background Davies-Unruh
bath. The implications are discussed.
