The weak arrow of time
In particle physics, charge conjugation (C), spatial inversion (P), and time reversal (T) are symmetry operations that can be made on states of SUOs. The CPT theorem asserts that the laws of physics are invariant to (unchanged by) the combined transformations acting on a state. It has been observed empirically that the laws of physics are not completely invariant to the partial operation CP in certain very subtle interactions [Christenson etal., 1964]. Therefore, if the CPT theorem is valid, the laws of physics are not completely invariant to time reversal. This therefore signals another arrow of time, known as the weak arrow of time. This exotic corner of physics may yet turn out to be of the greatest significance to our understanding of time and the universe, as it has been speculated to be behind the longstanding mystery of the observed enormous excess of matter over antimatter in our part of the universe.
The quantum arrow of time
There are two contrasting forms of time evolution in QM, known as unitary evolution and non-unitary evolution respectively. Unitary evolution describes how wavefunctions change in time if no information is being extracted by an observer. This form of evolution is theoretically reversible. Non-unitary evolution arises whenever an observer extracts empirical information: this form of evolution is irreversible because when an observation is made of some quantum outcome in an experiment, the corresponding wavefunction changes. In addition, the observer registers this information in their memory in one way or another and this is an irreversible process, defining the quantum arrow of time. Magnetic resonance imaging (MRI) is an increasingly important technique in chemistry, physics, and medicine that exploits both forms of quantum evolution to extract information about the internal structure of objects such as crystals and living tissue.