  If an asymmetry in time does not arise from the fundamental dynamical laws of
physics, it may be found in special boundary conditions. The argument normally
goes that since thermodynamic entropy in the past is lower than in the future
according to the Second Law of Thermodynamics, then tracing this back to the
time around the Big Bang means the universe must have started off in a state of
very low thermodynamic entropy: the Thermodynamic Past Hypothesis. In this
paper, we consider another boundary condition that plays a similar role, but
for the decoherent arrow of time, i.e. the quantum state of the universe is
more mixed in the future than in the past. According to what we call the
Entanglement Past Hypothesis, the initial quantum state of the universe had
very low entanglement entropy. We clarify the content of the Entanglement Past
Hypothesis, compare it with the Thermodynamic Past Hypothesis, and identify
some challenges and open questions for future research.
