  Understanding irreversibility in macrophysics from reversible microphysics
has been the holy grail in statistical physics ever since the mid-19th century.
Here the central question concerns the arrow of time, which boils down to
deriving macroscopic emergent irreversibility from microscopic reversible
equations of motion. As suggested by Boltzmann, this irreversibility amounts to
improbability (rather than impossibility) of the second-law-violating events.
Later studies suggest that this improbability arises from a fractal attractor
which is dynamically generated in phase space in reversible dissipative
systems. However, the same mechanism seems inapplicable to reversible
conservative systems, since a zero-volume fractal attractor is incompatible
with the nonzero phase-space volume, which is a constant of motion due to the
Liouville theorem. Here we demonstrate that in a Hamiltonian system the fractal
scaling emerges transiently over an intermediate length scale. Notably, this
transient fractality is unveiled by invoking the Loschmidt demon with an
imperfect accuracy. Moreover, we show that irreversibility from the fractality
can be evaluated by means of information theory and the fluctuation theorem.
The fractality provides a unified understanding of emergent irreversibility
over an intermediate time scale regardless of whether the underlying reversible
dynamics is dissipative or conservative.
