  We consider a very general class of theories, process theories, which capture
the underlying structure common to most theories of physics as we understand
them today (be they established, toy or speculative theories). Amongst these
theories, we will be focusing on those which are `causal', in the sense that
they are intrinsically compatible with the causal structure of space-time -- as
required by relativity. We demonstrate that there is a sharp contrast between
these theories and the corresponding time-reversed theories, where time is
taken to flow backwards from the future to the past. While the former typically
feature a rich gamut of allowed states, the latter only allow for a single
state: eternal noise. We illustrate this result by considering of the
time-reverse of quantum theory. We also derive a strengthening of the result in
PRL 108, 200403 on signalling in time-reversed theories.
