Category Archives: Talks I’ve attended

Maxwell’s Demon, Lions and semipermeable membranes

A few weeks ago I went to a talk based on 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.


The Sleeping Beauty paradox

Last week I went to a talk based on the following paper ( I didn’t really follow the argument that a quantum many-worlds version made the argument clearer, but it did get me thinking about the problem.

Beauty agrees to the following arrangement. After she goes to sleep on Sunday a coin is tossed. When she wakes up she is asked how likely it is that the coin landed heads – with the following proviso. If it landed heads she is just woken up on Monday, but if it is tails then after being woken on Monday she is hypnotised so she forgets that she has been woken up. She is then woken again on Tuesday with the same question. In no case does she know what day it is when she is woken up.

The paradox is that on Sunday she believes that the coin will land heads with a probability of 50%. She does not gain any new information when she is woken up, but if she makes a bet then the rational thing to do is to bet that is has landed heads with a probability of 33.3%.

When I came out of the talk I was convinced that the ‘correct’ probability had to be 50%. But then I began to construct an argument for this and I changed my mind – I now think that it is 33.3%

Suppose there were two ‘sleepers’ Peter and Paul. In fact they don’t have to sleep, you just arrange as follows. If the coin lands tails you ask each of them separately for the probability (so that the other doesn’t know about it), but if it lands heads then you just ask one of them at random. In this case a probability of 33.3% is certainly correct, but the person being asked has got some new information – the fact that he is being asked.

Suppose now that there is just one person, but the arrangement is that you hypnotise him to make him think that he is Peter or Paul – if the coin lands tails you ask each persona, if heads then just one at random. This seems equivalent to there being two people. Maybe you could just show him his ‘name’ on a card when he is woken up – but what difference could knowing the name make to the probability of the coin landing heads. So this must be just the same as with Beauty. Hence her correct choice of probability is 33.3%.

It seems to me that although in one sense Beauty does not gain any new information, in another she does, just as Peter or Paul gain new information when they are woken up and asked for the probability