  This review informs that the impossibility of genuine quantum time crystals
has been known in the C*-algebraic quantum statistical mechanics since 1970s.
The KMS condition implies that spontaneous breakdown of time-translation
symmetry is impossible in general quantum systems. In particular, any
non-trivial order, such as periodic, quasi-periodic, and chaotic order cannot
exist in the time direction of equilibrium states, meaning that genuine quantum
time crystals are excluded from the outset.
