A few weeks ago I went to a talk based on http://arxiv.org/abs/1003.0179. The argument is that in thermodynamics it is wrong to treat particles as indistinguishable. If you have two different kinds of particles in a container, then in principle it is possible to separate them using a semipermeable membrane, and so there is an entropy of mixing, no matter how small the difference is. Why should there be a discontinuity when the difference is reduced to zero?
Talk of semipermeable membranes made me think of the following:
Catching lions in the desert
The thermodynamic method: We construct a semi-permeable membrane which is permeable to everything except lions and sweep it across the desert. (H. Pétard 1938)
It is possible to accept Diek’s argument, thinking of the particles as being physically identical, but each having a unique identifier. The entropy would then be different to what it is normally taken to be, but you also need to think about how the distinguishabilty of the particles might be detected. There would need to be some sort of Maxwell’s demon, reading the identifier for each. There would be an entropy cost to this – according to Landauer’s principle it is when the demon needs to forget what it has read. This would presumably cancel out the difference in entropy in this model.
I once saw a pair of capercaillies in a wildlife park in an enclosure split into two parts. Between the two parts there was a hole which the female could get through, but the male, being considerably bigger could not. Hence the female got to choose whether she spent time with the male or not. So this is a semi-permeable membrane, differentiating one animal from another. Maybe the lion membrane isn’t so far fetched… But then to distinguish lions from everything else would need more than a hole of a given size, it would need a system which recognised lions – some sort of artificial intelligence.
My conclusion is that the claim that you can in principle find a semipermeable membrane to distinguish two different kinds of particles needs qualifying. When the difference is substantial it will be a matter of physics, but as the particles become more and more similar, distinguishing them becomes more of a matter of computation – which is thermodynamically different to using physics to distinguish them. This argues against the idea that physical processes can be thought of as computations – Some systems may be thought of as making choices, but a hole which allows some particles through and not others shouldn’t be thought of as a computational device.