  Birational rowmotion is a discrete dynamical system on the set of all
positive real-valued functions on a finite poset, which is a birational lift of
combinatorial rowmotion on order ideals. It is known that combinatorial
rowmotion for a minuscule poset has order equal to the Coxeter number, and
exhibits the file homomesy phenomenon for refined order ideal cardinality
statistic. In this paper we generalize these results to the birational setting.
Moreover, as a generalization of birational promotion on a product of two
chains, we introduce birational Coxeter-motion on minuscule posets, and prove
that it enjoys periodicity and file homomesy.
