  We analyze a mesoscopic conductor autonomously performing a thermodynamically
useful task, such as cooling or producing electrical power, in a part of the
system -- the working substance -- by exploiting another terminal or set of
terminals -- the resource -- that contains a stationary nonthermal
(nonequilibrium) distribution. Thanks to the nonthermal properties of the
resource, on average no exchange of particles or energy with the working
substance is required to fulfill the task. This resembles the action of a
demon, as long as only average quantities are considered. Here, we go beyond a
description based on average currents and investigate the role of fluctuations
in such a system. We show that a minimum level of entropy fluctuations in the
system is necessary, whenever one is exploiting a certain entropy production in
the resource terminal to perform a useful task in the working substance. For
concrete implementations of the demonic nonthermal engine in three- and
four-terminal electronic conductors in the quantum Hall regime, we compare the
resource fluctuations to the entropy production in the resource and to the
useful engine output (produced power or cooling power).
