## Effective Temperature of the Papers January 20, 2009

Posted by keithkchan in fun stuffs, Statistial Physics, Whatever.

Today when I listened to my colleague tidying up the papers from the printer so that he could staple them neatly, I came up with an idea that we can probably define some effective temperature to characterize how neat the system is.

OK, let me state the problem more clearly. For example when you print an article, the papers from the printer do not completely line up. So usually we will take them up a little bit and release it. (It is hard to describe it, but I suppose you know what I mean.) Usually we do it a few times, until we are satisfied with the neatness. What I am interested in is that how many times is “good enough”. Clearly after doing it 100 times will not be better than 10 times since the system is in equilibrium, and subsequently there will be fluctuations about the equilibrium. I think we can define an effective temperature for the system, and from which we can extract the fluctuation. I expect how fast the equilibrium can be achieved depends on the textures of the papers, and the number of pages.

I was not sure if somebody had come up with similar ideas before. I was so excited (maybe crazy) that I even talked to Paul Chaikin about my idea. You know Chaikin likes to pack M & M chocolates. He was busy and did not seem to be very enthusiastic. In particular, he cautioned that there were many ways to define the effective temperature, which may or may not be meaningful in this kind of non-thermodynamic system. One way to define the effective temperature of the system of papers is to calculate the root-mean-square (RMS) of the papers from the centroid of the system.

I agree that the definition of the effective temperature is not unique, may even be arbitrary to some extent. Besides that, there are some arbitrariness in the each padding process if it is done by hands. If it is done by machines, machines probably can do it “perfectly”, and it does not address my original motivation, i.e. tidying up papers by hands.

It does not seem to me this problem will yield anything more than satisfying my curiosity, and I have many other things to do, thus I don’t think I will pursue it further unless somebody is also interested in and want to do something crazy. But at least this problem manages to become a post on the Blackboard.