%A A.P. Horsfield %A D.R. Bowler %A A.J. Fisher %X We present a time-dependent method based on the single-particle electron density matrix that allows the electronic and ionic degrees of freedom to be modelled within the Ehrenfest approximation in the presence of open boundaries. We describe a practical implementation using tight binding, and use it to investigate steady-state conduction through a single-atom device and to perform molecular dynamics. We find that in the Ehrenfest approximation an electric current allows both ionic heating and cooling to take place, depending on the bias. %J Journal of Physics: Condensed Matter %T Open-boundary Ehrenfest molecular dynamics: towards a model of current unduced heating in nanowires %O Letter to the editor. %D 2004 %N 7 %V 16 %P L65-L72 %L discovery460