  We study the locality of the acceleration temperature in the Unruh effect. To
this end, we develop a new formalism for the modeling of macroscopic
irreversible detectors. In particular, the formalism allows for the derivation
of the higher-order coherence functions, analogous to the ones employed in
quantum optics, that encode temporal fluctuations and correlations in particle
detection. We derive a causal and approximately local-in-time expression for an
Unruh-Dewitt detector moving in a general path in Minkowski spacetime.
Moreover, we derive the second-order coherence function for uniformly
accelerated Unruh-Dewitt detectors. We find that the fluctuations in detection
time for a single Unruh-Dewitt detector are thermal. However, the correlations
in detection-time between two Unruh-Dewitt detectors with the same acceleration
but separated by a finite distance are not thermal. This result suggests that
the Unruh effect is fundamentally local, in the sense that the notion of
acceleration temperature applies only to the properties of local field
observables.
