The connection between the micro and macro-arrow of time is discussed in the frame of the stochastic quantum hydrodynamic analogy (SQHA). The presence of fluctuations that in the case on non-linear interactions leads to the breaking of the quantum mechanics on large scale and then to the macroscopic irreversibility with a defined arrow of time, gives also rise to the time reversal breaking in the micro-scale quantum evolution (micro-arrow of time). The quantum irreversibility with time reversal asymmetry is briefly discussed.
The connection between the micro and macro-arrow of time is discussed in the frame of the stochastic quantum hydrodynamic analogy. The presence of fluctuations that in the case on non-linear interactions leads to the breaking of the quantum mechanics on large scale and then to the macroscopic irreversibility and arrow of time, gives also rise to the time reversal breaking in the micro-scale quantum stochastic evolution (micro-arrow of time). The quantum irreversibility and the theoretical tools to calculate the time reversal asymmetry in the elementary particle decays are briefly discussed.