  The achievement of local cooling is a prominent goal in the design of
functional transport nanojunctions. One generic mechanism for local cooling is
driving a system through a local uphill potential step. In this paper we
examine the manifestation of this mechanism in the context of the Kramers
barrier crossing problem. For a particle crossing a barrier, the local
effective temperature and the local energy exchange with the thermal
environment are calculated, and the coefficient of performance of the ensuing
cooling process is evaluated.
