  In this article, we introduce two kinds of Fluctuation Theorems (FT)
containing information for autonomous Maxwell's demon-assisted machines. Using
Jensen's Inequality, we obtain Landauer's principle formulation of the second
law for the whole process of the machine. Finally we make use of our results to
analyze a new information device. \pacs{05.70.Ln, 05.40.-a, 89.70.Cf}
