Abstract

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. Source coding consists of generating a description of a sequence shorter than its original representation, ideally reducing its size to its information content: the more ordered a sequence is, the lower its information content and the shorter its encoding. Here, we describe how source coding enables the quantification of order in non-equilibrium and equilibrium many-body systems, both discrete and continuous, even when the underlying form of order is unknown. We consider absorbing state models, such as Manna, Conserved Lattice Gas and a continuum model of Random Organization, as well as a system of Brownian active particles undergoing motility-induced phase separation. Using a universal lossless data compression algorithm to analyse the configurations of this broad class of systems, we show how our approach can reliably identify non-equilibrium phase transitions, determine their character, and 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, to cosmology and biology.