Then you put the tea and the water in thermal contact. Now, for every possible microstate of the glass of water, the combined system evolves to a single final microstate (only one, because you know the exact state of the tea).
After you put the glass of water in contact with the cup of tea, you will quickly become uncertain about the state of the tea. In order to still know the microstate, you need to be fed more information.
If you have a Boltzmann distribution, you still know all the microstates—you just have a probability distribution over them. Time evolution in contact with a zero-entropy object moves probability from one microstate to another in a predictable way, with neither compression nor spreading of the probability distribution.
Sure, this requires obscene amounts of processing power to keep track of, but not particularly more than it took to play Maxwell’s demon with a known cup of tea.
After you put the glass of water in contact with the cup of tea, you will quickly become uncertain about the state of the tea. In order to still know the microstate, you need to be fed more information.
If you have a Boltzmann distribution, you still know all the microstates—you just have a probability distribution over them. Time evolution in contact with a zero-entropy object moves probability from one microstate to another in a predictable way, with neither compression nor spreading of the probability distribution.
Sure, this requires obscene amounts of processing power to keep track of, but not particularly more than it took to play Maxwell’s demon with a known cup of tea.