  Many dynamical phenomena in complex systems concern spreading that plays out
on top of networks with changing architecture over time -- commonly known as
temporal networks. A complex system's proneness to facilitate spreading
phenomena, which we abbreviate as its `spreading vulnerability', is often
surmised to be related to the topology of the temporal network featured by the
system. Yet, cleanly extracting spreading vulnerability of a complex system
directly from the topological information of the temporal network remains a
challenge. Here, using data from a diverse set of real-world complex systems,
we develop the `entropy of temporal entanglement' as a novel and insightful
quantity to measure topological complexities of temporal networks. We show that
this parameter-free quantity naturally allows for topological comparisons
across vastly different complex systems. Importantly, by simulating three
different types of stochastic dynamical processes playing out on top of
temporal networks, we demonstrate that the entropy of temporal entanglement
serves as a quantitative embodiment of the systems' spreading vulnerability,
irrespective of the details of the processes. In being able to do so, i.e., in
being able to quantitatively extract a complex system's proneness to facilitate
spreading phenomena from topology, this entropic measure opens itself for
applications in a wide variety of natural, social, biological and engineered
systems.
