Fisher's arrow of "time" in cosmological coherent phase space

Fisher's arrow of "time" in a cosmological phase space defined as in quantum optics (i.e. whose points are coherent states) is introduced as follows. Assuming that the phase space evolution of the universe starts from an initial squeezed cosmological state towards a final thermal one, a Fokker-Planck equation for the time-dependent, cosmological Q phase space probability distribution can be written down. Next, using some recent results in the literature, we derive an information arrow of time for the Fisher phase space cosmological entropy based on the Q-function. We also mention the application of Fisher's arrow of time to stochastic inflation models.