The problem of quantum measurement can be partially resolved by incorporating a process of spontaneous disentanglement into quantum dynamics. We propose a modified master equation, which contains a nonlinear term giving rise to both spontaneous disentanglement and thermalisation. We find that the added nonlinear term enables limit cycle steady states, which are prohibited in standard quantum mechanics. This finding suggests that an experimental observation of such a limit cycle steady state can provide an important evidence supporting the spontaneous disentanglement hypothesis.