  Many empirical studies have revealed that the occurrences of contacts
associated with human activities are non-Markovian temporal processes with a
heavy tailed inter-event time distribution. Besides, there has been increasing
empirical evidence that the infection and recovery rates are time-dependent.
However, we lack a comprehensive framework to analyze and understand
non-Markovian contact and spreading processes on temporal networks. In this
paper, we propose a general formalism to study non-Markovian dynamics on
non-Markovian temporal networks. We find that, under certain conditions,
non-Markovian dynamics on temporal networks are equivalent to Markovian
dynamics on static networks. Interestingly, this result is independent of the
underlying network topology.
