  This paper is concerned with certain invariant random processes (called
factors of IID) on infinite trees. Given such a process, one can assign
entropies to different finite subgraphs of the tree. There are linear
inequalities between these entropies that hold for any factor of IID process
(e.g. "edge versus vertex" or "star versus edge"). These inequalities turned
out to be very useful: they have several applications already, the most recent
one is the Backhausz-Szegedy result on the eigenvectors of random regular
graphs.
  We present new entropy inequalities in this paper. In fact, our approach
provides a general "recipe" for how to find and prove such inequalities. Our
key tool is a generalization of the edge-vertex inequality for a broader class
of factor processes with fewer symmetries.
