Entropic Dynamics (2)

Today I want to comment a paper by John Cardy. He was a postdoc with my thesis advisor Bob Sugar at UCSB. At that time John was working on Reggeon Field Theory. He came from England to California, and eventually he became a Professor at Oxford.

Recently he, and coworkers, published a beautiful paper:

Universal amplitude ratios of two-dimensional percolation from field theory

He can exactly calculate a numerical ratio:

                         1/2
            _          _
            |   40    |
R_ξt⁺ = |-----------|
           |_27 √3 _|

This number can be measured experimentally, and both results are in good agreement.

My point here is that Percolation Theory, is one of the most "geometrical" theories of Statistical Mechanics. It is the geometric structure of space which tells us how particles move statistically. You give me a three-dimensional description of space, and I tell you how a group of particles will move there. And I mean, real barriers in the way, corridors, orifices, what have you. Particles will find their way through that maze and will come out on the other side. To put it in other words. You have coffee grains in coffee makers, you pour hot water on the one side, and down there you'll get a coffee infusion. Water molecules found a way to move through the maze, and come on the other side with coffee particles attached. The water becomes black, and you have coffee.

Thanks to the bright minds of people like John, now we can exactly calculate the best predictions  theory can give. When that happens we say that we understand.

Entropic Dynamics is the study of motion then, when the complexity of the environment produces statsitical motion. What I mean by that is that uncertainty is vanquished to the extent allowed by probability theory, as envisioned around two hundred years ago, by Pascal and Fermat, when they analyzed wagers.