There is a connection between the uncertainty principle and the second law of thermo dynamics, but it's not necessary or strong. Boltsman understood the second law without knowing anything about the uncertainty principle. When you're mixing cream into coffee, you're not in that regime. There's no importance in a quantum of facts or the uncertainty principle, or anything like that. And by the way, i say this over and over again, but the arrow of time is explained. Explained by the definition that we have of entropy from boltsman,. The fact that the early universe was low. Those two things together explain the arrow ofTime.