Quantifying hidden order out of equilibrium*

While the equilibrium properties, states, and phase transitions of interacting systems are well described by statistical mechanics, the lack of suitable state parameters has hindered the understanding of non-equilibrium phenomena in diverse settings, from glasses to driven systems to biology. Here, we describe a simple idea enabling the quantification of order in non-equilibrium and equilibrium systems, both discrete and continuous, even when the underlying form of order is unknown. The length of a losslessly compressed data file is a direct measure of its information content, a quantity directly related to a system's entropy. Using data compression to study several out-of-equilibrium systems, we show that our approach is capable of reliably identifying dynamical phase transitions and their character, and to quantitatively predict certain critical exponents, without any knowledge of the relevant order parameters. This approach thus provides a new and essential way of quantifying order in systems ranging from condensed matter systems in and out of equilibrium, to cosmology and biology.