 Another claim about the significance of decoherence relates to time asymmetry (see e.g. the entries on  time asymmetry in thermodynamics  and  philosophy of statistical mechanics).  Insofar as apparent collapse (branching) is indeed a time-directed process, decoherence will have direct relevance to the emergence of this ‘quantum mechanical arrow of time’. This is not a straightforward issue, however, and questions familiar from the foundations of statistical mechanics arise also in the context of decoherence. Specific issues include the fact that models of environmental decoherence tend to assume very special (unentangled) initial conditions, and the fact that the definition of the decoherence functional in the histories approach is itself asymmetrical (although symmetric versions also exist). For a spectrum of discussions, see Hartle (1998, and references therein), Zeh (2001, Chapter 4), and Bacciagaluppi (2002, Section 6.1; 2007). Whether decoherence is connected to the other familiar arrows of time is a more specific question. Indeed, should decoherence allow us to recover the time-symmetric classical description of, say, particle trajectories in a gas, or does it allow us to derive time-asymmetric thermodynamic behaviour directly, by-passing classical attempts at understanding it? Note that insofar as classical systems such as gases are believed to be chaotic, the origin of the probabilities in classical statistical mechanics will arguably be quantum. For various discussions, see e.g. Zurek and Paz (1994), Hemmo and Shenker (2001), and Wallace (2012a, Chapter 9; and 2001, 2013a, 2013b in the  Other Internet Resources).  