Taking a song someone else composed, and changing the style dramatically, possibly even adding entirely new elements or musical sections. Can include limited cases of medley, if all songs present are changed dramatically. Note: Changing instruments or adding a drum beat alone does not constitute a remix (See: Complete Idiot).
A remix is an alternative version of a song, different from the original version. A record producer or audio engineer uses audio mixing to compose an alternate master of a song, adding or subtracting elements, or simply changing the equalization, dynamics, pitch, tempo, playing time, or almost any other aspect of the various musical components. Usually, a remix will involve substantial changes to the arrangement of a recorded work; lyrics may be added or removed, such alterations are not a necessity.