The time evolution of fluctuation algebra in mean field theories

Fluctuation algebra is defined for equilibrium states of mean field theories. The time evolution is calculated; and, in contrast to interactions with finite range, the fluctuation algebra is not in a KMS state with respect to this time evolution though the underlying quasilocal state. If the system is coupled to an other system mimicking a laser then the evolution depends on the underlying mean field theory and shows varying large time behaviour, so that the fluctuations either rotate or increase linearly or exponentially in time, in correspondence to the stability of the underlying quasilocal state.