  All the laws of physics are time-reversible. Time arrow emerges only when
ensembles of classical particles are treated probabilistically, outside of
physics laws, and the entropy and the second law of thermodynamics are
introduced. In quantum physics, no mechanism for a time arrow has been proposed
despite its intrinsic probabilistic nature. In consequence, one cannot explain
why an electron in an excited state will "spontaneously" transition into a
ground state as a photon is created and emitted, instead of continuing in its
reversible unitary evolution. To address such phenomena, we introduce an
entropy for quantum physics, which will conduce to the emergence of a time
arrow.
  The entropy is a measure of randomness over the degrees of freedom of a
quantum state. It is dimensionless; it is a relativistic scalar, it is
invariant under coordinate transformation of position and momentum that
maintain conjugate properties and under CPT transformations; and its minimum is
positive due to the uncertainty principle.
  To excogitate why some quantum physical processes cannot take place even
though they obey conservation laws, we partition the set of all evolutions of
an initial state into four blocks, based on whether the entropy is (i)
increasing but not a constant, (ii) decreasing but not a constant, (iii) a
constant, (iv) oscillating. We propose a law that in quantum physics entropy
(weakly) increases over time. Thus, evolutions in the set (ii) are disallowed,
and evolutions in set (iv) are barred from completing an oscillation period by
instantaneously transitioning to a new state. This law for quantum physics
limits physical scenarios beyond conservation laws, providing causality
reasoning by defining a time arrow.
