  The asymmetry properties of a state relative to some symmetry group specify
how and to what extent the given symmetry is broken by the state.
Characterizing these is found to be surprisingly useful for addressing a very
common problem: to determine what follows from a system's dynamics (possibly
open) having that symmetry. We demonstrate and exploit the fact that the
asymmetry properties of a state can be understood in terms of
information-theoretic concepts. We show that for a pure state psi and a
symmetry group G, they are completely specified by the characteristic function
of the state, defined as chi_psi(g)=<psi|U(g)|psi> where g\in G and U is the
unitary representation of interest. Based on this observation, we study several
important problems about the interconversion of pure states under symmetric
dynamics such as determining the conditions for reversible transformations,
deterministic irreversible transformations and asymptotic transformations.
