  Arrows of time - thermodynamical, cosmological, electromagnetic, quantum
mechanical, psychological - are basic properties of Nature. For a quantum
system-bath closed system the de-correlated initial conditions and no-memory
(Markovian) dynamics are outlined as necessary conditions for the appearance of
the thermodynamical arrow. The emergence of the arrow for the system evolving
according to non-unitary dynamics due to the presence of the bath, then, is a
result of limited observability, and we conjecture the arrow in the observable
Universe as determined by the dark sector acting as a bath. The voids in the
large scale matter distribution induce hyperbolicity of the null geodesics,
with possible observational consequences.
