Abstract
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.
Highlights
The breaking of quantum coherence and the quantum to classical phase transition are problems that have many consequences in all problems of physics whose scale is larger than that one of small atoms
The arrow of time in the classical kinetics is commonly ascribed to the transition from the molecular scale to the macroscopic one united to the presence of a small initial incertitude in a system with a huge number of non-linearly interacting particles [1].Even if the time reversal symmetry breaking has been observed for the probability transition in some elementary particle decay [2], the macroscopic arrow of time has no connection with the nature of the quantum mechanics
The author has developed the stochastic version of the quantum hydrodynamic analogy (SQHA) [3] that comprehends both the standard quantum mechanics as the deterministic limit of the theory and the classical stochastic mechanics as the large-scale limit
Summary
The breaking of quantum coherence and the quantum to classical phase transition are problems that have many consequences in all problems of physics whose scale is larger than that one of small atoms. Both the equations of quantum and the classical mechanics own the time-reversal symmetry.
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