  We study the role of ensemble averaging in holography by exploring the
relation between the universal late time behavior of the spectral form factor
and the second Renyi entropy of a thermal mixed state of the doubled system.
Both quantities receive contributions from wormhole saddle-points: in the
former case they lead to non-factorization while in the latter context they
quantify decoherence due to the interaction with an environment. Our reasoning
indicates that the space-time continuity responsible for non-factorization and
space-time continuity through entanglement are in direct competition with each
other. In an accompanying paper, we examine this dual relationship in a general
class of 1D quantum systems with the help of a simple geometric path integral
prescription.
