A number of recent theoretical investigations of electron motion in attaching gases demonstrate the possibility of a steady-state situation in which the electric current opposes the applied field. This phenomenon, which has been called "negative absolute electron mobility", implies a Joule cooling effect and an associated negative entropy production, suggesting, at first glance, a possible violation of the second law of thermodynamics. In this article we show that the entropy production has in fact two components, the expected negative contribution due to "Joule cooling," and an additional positive part arising from "attachment heating." We insist that the total entropy production be positive, in accordance with the second law, and this has the practical implication that the measurable ("bulk") electron drift velocity must always be positive, even though the actual average ("flux") velocity may be negative. We discuss the phenomenon physically and take as a numerical example electrons in Ar/F-2 mixtures, using Monte Carlo simulation and approximate momentum transfer theory methods to highlight the distinction between the two types of transport coefficient. (C) 2003 American Institute of Physics.