The 1/f fluctuation is ubiquitously observed in nature and has attracted general interest over the past few decades. In this talk we concentrate on collective motion in large Hamiltonian systems having long-range interactions and propose a scenario to explain the 1/f fluctuation by using the pseudo-Casimir-invariants. The scenario is supported by systematic numerical simulations .
 Y. Y. Yamaguchi and K. Kaneko, Collective 1/f fluctuation by pseudo-Casimir-invariants, Phys. Rev. E 98, 020201(R) (2018).