  Recently, several studies involving open quantum systems which possess a
strong symmetry have observed that every individual trajectory in the Monte
Carlo unravelling of the master equation will dynamically select a specific
symmetry sector to freeze into in the long-time limit. This phenomenon has been
termed dissipative freezing, and in this paper we argue, by presenting several
simple mathematical perspectives on the problem, that it is a general
consequence of the presence of a strong symmetry in an open system with only a
few exceptions. Using a number of example systems we illustrate these
arguments, uncovering an explicit relationship between the spectral properties
of the Liouvillian in off-diagonal symmetry sectors and the time it takes for
freezing to occur. In the limiting case that eigenmodes with purely imaginary
eigenvalues are manifest in these sectors, freezing fails to occur. Such modes
indicate the preservation of information and coherences between symmetry
sectors of the system and can lead to phenomena such as non-stationarity and
synchronisation. The absence of freezing at the level of a single quantum
trajectory provides a simple, computationally efficient way of identifying
these traceless modes.
