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Manfred comments on Open Thread, Feb. 2 - Feb 8, 2015 - Less Wrong Discussion
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Oh, I see, you're thinking of particle exchange, like if one dumped the water into the tea. This case is not what I intended - by thermal contact I just mean exchange of energy.
With identical particles, the case with particle exchange gets complicated. There might even be some interesting physics there.
The thermodynamics of energy exchange and mass exchange are actually similar. You still get the increase in entropy, even if you are just exchanging energy.
One the one hand, this is a good point that points out a weakness in my argument - if states are continuous rather than discrete, one can increase or decrease entropy even with deterministic time-evolution by spreading out or squeezing probability mass.
But I don't know how far outside the microcanonical this analogy you're making holds. Exchanging energy definitely works like exchanging particles when all you know is the total energy, but there's no entropy increase when both are in a single microstate, or when both have the same Boltzmann distribution (hm, or is there?).
I'll think about it too.