It might be expected that the existence of automorphisms of the \(C^*\)- algebra A of quantum statistics that commute with the time automorphism, can give some insight into ergodic properties, as the existence of independent constants of motion do in classical dynamics. It turns out that the question whether such automorphisms exist cannot be decided on the level of the von Neumann algebra corresponding to the representation of A in some equilibrium state: in contrary: as all modular automorphisms of a von Neumann algebra are connected by inner cocycles, it is also possible to find to any automorphism group \(\sigma\) that commutes with some modular automorphism group \(\alpha_ t\) an inner cocycle such that the resulting automorphism group \({\bar \sigma}\) commutes with another given modular automorphism group \({\bar \alpha}{}_ t\).