  For a certain class of isolated quantum systems, we report the existence of
irreversible processes in which the energy is not dissipated. After a closed
cycle in which the initial energy distribution is fully recovered, the
expectation value of a symmetry-breaking observable changes from a value
different from zero in the initial state, to zero in the final state. This
entails the unavoidable loss of a certain amount of information, and
constitutes a source of irreversibility. We show that the von Neumann entropy
of time-averaged equilibrium states increases in the same magnitude as a
consequence of the process. We support this result by means of numerical
calculations in an experimentally feasible system, the Lipkin-Meshkov-Glick
model.
