  Using a combination of molecular dynamics simulations and fundamental
statistical mechanics, we analyze the position and velocity distribution of a
trapped ion immersed in two ideal gases at differing temperatures. Such a
system has been realized in the recently developed MOTion trap architecture.
This system has the potential to serve as platform for studying nonequilibrium
statistical mechanics in a controlled environment. As examples, we demonstrate
a non-Maxwell Boltzmann velocity ionic distribution in the trap, the breakdown
of the fluctuation-dissipation theorem, and position-velocity sorting, wherein
high-velocity ionic states are over represented at points of high potential
energy. We propose experiments to test these predictions.
