  We derive the temporal renormalisation group flow of the energy-momentum
tensor at the example of a general scalar theory. The local causal structure of
the temporal renormalisation group flow allows to monitor and control
causality, unitarity and general conservation laws at each infinitesimal
renormalisation group step. We explore energy-conserving truncations in a
comparison of generic flows and the causal temporal flow of the energy-momentum
tensor. We also observe that the temporal regulator preserves scale invariance,
which is violated for generic momentum regulators. Specifically we discuss the
relation of these terms to the trace anomaly of the energy-momentum tensor.
Moreover, we show that the causal temporal flow of the energy-momentum tensor
can be integrated analytically, and demonstrate, that the result is consistent
with energy conservation.
