  Recent research has highlighted limitations of studying complex systems with
time-varying topologies from the perspective of static, time-aggregated
networks. Non-Markovian characteristics resulting from the ordering of
interactions in temporal networks were identified as one important mechanism
that alters causality, and affects dynamical processes. So far, an analytical
explanation for this phenomenon and for the significant variations observed
across different systems is missing. Here we introduce a methodology that
allows to analytically predict causality-driven changes of diffusion speed in
non-Markovian temporal networks. Validating our predictions in six data sets,
we show that - compared to the time-aggregated network - non-Markovian
characteristics can lead to both a slow-down, or speed-up of diffusion which
can even outweigh the decelerating effect of community structures in the static
topology. Thus, non-Markovian properties of temporal networks constitute an
important additional dimension of complexity in time-varying complex systems.
