[jbay808]

If the cup of water is in a specific microstate at time t=0, and evolves over time according to deterministic equations of motion, how will it "access" other microstates that aren't along that specific trajectory in phase-space?

[deltaonefour]

It can't. But you're not typically defining ONLY microstates along that trajectory as accessible. You are defining all accessible configurations according to your defined macrostate.

Knowledge of future microstates does not change what was already defined as a macrostate. The definition and the rules you used to construct a macrostate are independent to knowledge of the system.

If you gain knowledge of the system and you would like to change your macrostate, then be my guest. You can certainly do that, but "entropy" as we know it does not actually change with more knowledge unless you change the parameters according to your gained knowledge.

Think of it this way. The thermometer ALWAYS reads the same thing EVEN if you have 100% knowledge of the current microstate. You can build a new thermometer using some other mechanism to get a different reading and to take advantage of your new found knowledge... but you'd be changing the definition of your macrostate.