Paul Chaikin

Quantifying hidden order 

We introduce a simple idea enabling the quantification of organization in non-equilibrium and equilibrium systems, even when the form of order is unknown. The length of a losslessly compressed data file is a direct measure of its information content. We use lossless data compression, and more recently pattern matching, Shannon entropy approximates, to study several equilibrium and out-of-equilibrium systems, and show that they identify ordering, phase transitions, critical behavior, and critical exponents in thermodynamic and dynamic transitions. Our technique should provide a quantitative measure of organization in both experimental and model systems. More recently we have demonstrated that similar techniques can reveal local entropy production and the ability to extract work from non-equilibrium systems. In our study of dynamical phase transitions, we also stumbled across some interesting results on the hyperuniformity of “random” packings.