One of the explanations of the second law of thermodynamics is that it goes back to the low entropy in the early universe (How do you prove the second law of thermodynamics from statistical mechanics?). My question is: assuming that's true how does it filter down to everyday occurrences where we see glasses getting broken but not becoming whole, cups of coffee cooling off but not heating up by cooling air, and so on?
The equations of Hamiltonian dynamics are time symmetric, so whatever evolution it allows it also allows the same in reverse, which we do not observe. What is the mechanism that converts low entropy condition in the distant past to the dominance of entropy increasing evolutions in our surroundings? Even assuming that the overall entropy increases shouldn't there be observed instances where the opposite happens locally from time to time, even on a macroscopic scale? To put it another way, why is the state of local systems today so heavily dependent on the condition of the universe as a whole billions of years ago? Why can't we isolate a macroscopic system enough from whatever influence the early universe exerts on it, and have it exhibit entropy decrease?
Note: I am aware of another explanation of the second law based on low probability in some sense of entropy decreasing evolutions (Is the second law of thermodynamics a fundamental law, or does it emerge from other laws?), but it seems to have other problems, so I'd like to know if there is an explanation from the early universe point of view.