Title: Quantifying hidden order out of equilibrium

Author (Talk): Stefano Martiniani, New York University (NYU)

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 will 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.