  Many non-equilibrium, active processes are observed at a coarse-grained
level, where different microscopic configurations are projected onto the same
observable state. Such "lumped" observables display memory, and in many cases
the irreversible character of the underlying microscopic dynamics becomes
blurred, e.g., when the projection hides dissipative cycles. As a result, the
observations appear less irreversible, and it is very challenging to infer the
degree of broken time-reversal symmetry. Here we show, contrary to intuition,
that by ignoring parts of the already coarse-grained state space we may -- via
a process called milestoning -- improve entropy-production estimates.
Milestoning systematically renders observations "closer to underlying
microscopic dynamics" and thereby improves thermodynamic inference from lumped
data assuming a given range of memory. Moreover, whereas the correct general
physical definition of time-reversal in the presence of memory remains unknown,
we here show by means of systematic, physically relevant examples that at least
for semi-Markov processes of first and second order, waiting-time contributions
arising from adopting a naive Markovian definition of time-reversal generally
must be discarded.
