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 nonequilibrium phenomena in diverse settings, from glasses to driven systems to biology. The length of a losslessly compressed data file is a direct measure of its information content: The more ordered the data file is, the lower its information content and the shorter the length of its encoding can be made. Here, we describe how data compression enables the quantification of order in nonequilibrium and equilibrium many-body systems, both discrete and continuous, even when the underlying form of order is unknown. We consider absorbing state models on and off lattice, as well as a system of active Brownian particles undergoing motility-induced phase separation. The technique reliably identifies nonequilibrium phase transitions, determines their character, quantitatively predicts certain critical exponents without prior knowledge of the order parameters, and reveals previously unknown ordering phenomena. This technique should provide a quantitative measure of organization in condensed matter and other systems exhibiting collective phase transitions in and out of equilibrium.
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We would like to thank Mark Adler, Daniel Hexner, Yariv Kafri, Johannes Klicpera, Yuval Lemberg, Neri Merhav, Emre Telatar, and Adi Wyner for interesting and useful discussions. We thank Ron Alfia for preliminary numerical results. We are grateful to Ram Avinery, Roy Beck, and Micha Kornreich for useful discussions and for providing their preprint on the application of data compression to study protein folding . This work was primarily supported by the National Science Foundation Physics of Living Systems Grant No. 1504867. D. L. thanks the U.S.-Israel Binational Science Foundation (Grant No. 2014713), the Israel Science Foundation (Grant No. 1866/16), and the Initiative for the Theoretical Sciences at the Graduate Center of CUNY. P. M. C. was supported partially by the Materials Research Science and Engineering Center (MRSEC) Program of the National Science Foundation under Grant No. DMR-1420073.
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