  We prove that a topologically predictable action of a countable amenable
group has zero topological entropy, as conjectured by Hochman. On route, we
investigate invariant random orders and formulate a unified Kieffer-Pinsker
formula for the Kolmogorov-Sinai entropy of measure preserving actions of
amenable groups. We also present a proof due to Weiss for the fact that
topologically prime actions of sofic groups have non-positive topological sofic
entropy.
