We describe a new class of models of quantum space-time based on energetic causal sets and show that under natural conditions space-time emerges from them. These are causal sets whose causal links are labeled by energy and momentum and conservation laws are applied at events. The models are motivated by principles we propose govern microscopic physics which posit a fundamental irreversibility of time. One consequence is that each event in the history of the universe has a distinct causal relationship to the rest; this requires a novel form of dynamics which can be applied to uniquely distinctive events. We hence introduce a new kind of deterministic dynamics for a causal set in which new events are generated from pairs of progenitor events by a rule which is based on extremizing the distinctions between causal past sets of events. This dynamics is asymmetric in time, but we find evidence from numerical simulations of a $1+1$ dimensional model, that an effective dynamics emerges which restores approximate time reversal symmetry. Finally we also present a natural twistorial representation of energetic causal sets.