From measurements of thermally driven flux-vortex motion (flux-flow Nernst effect) in an epitaxial YBa{sub 2}Cu{sub 3}O{sub 7} film we determine the entropy {ital S}{sub {phi}} transported by a moving vortex and demonstrate agreement with recent Ettingshausen-effect results. Because a Nernst effect is a distinctive signature of vortex motion in a superconductor, this experiment also reveals the field and temperature regions of the mixed state in which vortices move freely. We can therefore correlate these measurements with other transport studies of the mixed state.