We derive a fluctuation theorem to describe entropy fluctuations in steady
states of systems with density gradients due to open boundaries. The fluctu
ations are related to the growth rate of the phase-space density, instead o
f the phase-space contraction rate. Explicit derivations are presented for
a multibaker map, but the arguments are rather general, and should hold for
a much wider class of dynamical systems. A comparison with recent results
for stochastic systems is also given.