  Simple examples are used to introduce and examine symmetries of open quantum
dynamics that can be described by unitary operators. For the Hamiltonian
dynamics of an entire closed system, the symmetry takes the expected form
which, when the Hamiltonian has a lower bound, says that the unitary symmetry
operator commutes with the Hamiltonian operator. There are many more symmetries
that are only for the open dynamics of a subsystem. Examples show how these
symmetries alone can reveal properties of the dynamics and reduce what needs to
be done to work out the dynamics. A symmetry of the open dynamics of a
subsystem can even imply properties of the dynamics for the entire system that
are not implied by the symmetries of the dynamics of the entire system. The
symmetries are generally not related to constants of the motion for the open
dynamics of the subsystem. There are many symmetries that cannot be seen in the
Schrodinger picture as symmetries of dynamical maps of density matrices for the
subsystem.
  There are symmetries of the open dynamics of a subsystem that depend only on
the dynamics. In the simplest examples, these are also symmetries of the
dynamics of the entire system. There are many more symmetries, of a new kind,
that also depend on correlations, or absence of correlations, between the
subsystem and the rest of the entire system, or on the state of the rest of the
entire system.
