  We investigate the radiative processes involving two entangled Unruh-DeWitt
detectors that are moving on circular trajectories in $(2+1)$-dimensional
Minkowski spacetime. We assume that the detectors are coupled to a massless,
quantum scalar field, and calculate the transition probability rates of the
detectors in the Minkowski vacuum as well as in a thermal bath. We also
evaluate the transition probability rates of the detectors when they are
switched on for a finite time interval with the aid of a Gaussian switching
function. We begin by examining the response of a single detector before we go
on to consider the case of two entangled detectors. As we shall see, working in
$(2+1)$ spacetime dimensions makes the computations of the transition
probability rates of the detectors relatively simpler. We find that the cross
transition probability rates of the two entangled detectors can be comparable
to the auto transition probability rates of the individual detectors. We
discuss specific characteristics of the response of the entangled detectors for
different values of the parameters involved and highlight the effects of the
thermal bath as well as switching on the detector for a finite time interval.
