  We numerically exhibit strange scaling and temporal evolution of finite-size
fluctuation in thermal equilibrium of a simple long-range interacting system.
These phenomena are explained from the view point of existence of the Casimirs
and their nonexactness in finite-size systems, where the Casimirs are
invariants in the Vlasov dynamics describing the long-range systems in the
limit of large population. This explanation expects appearance of the reported
phenomena in a wide class of isolated long-range systems. The scaling theory is
also discussed as an application of the strange scaling.
