biostudies-literatureLi HChinese Academy of SciencesNational Natural Science Foundation of ChinaChina Postdoctoral Science Foundatione2017392118https://www.ebi.ac.uk/biostudies/studies/S-EPMC7980390biostudies-literatureUnknown118(11)Apparent critical phenomena, typically indicated by growing correlation lengths and dynamical slowing down, are ubiquitous in nonequilibrium systems such as supercooled liquids, amorphous solids, active matter, and spin glasses. It is often challenging to determine if such observations are related to a true second-order phase transition as in the equilibrium case or simply a crossover and even more so to measure the associated critical exponents. Here we show that the simulation results of a hard-sphere glass in three dimensions are consistent with the recent theoretical prediction of a Gardner transition, a continuous nonequilibrium phase transition. Using a hybrid molecular simulation-machine learning approach, we obtain scaling laws for both finite-size and aging effects and determine tProceedings of the National Academy of Sciences of the United States of AmericaDetermining the nonequilibrium criticality of a Gardner transition via a hybrid study of molecular simulations and machine learning.PMC7980390Project 22073004Project 119350022018M641141Project 11947302Project 21622401Grant NO. ZDBS-LY-7017Project 11974361Jiang YLi HChen JZYJin YfalseDetermining the nonequilibrium criticality of a Gardner transition via a hybrid study of molecular simulations and machine learning.Apparent critical phenomena, typically indicated by growing correlation lengths and dynamical slowing down, are ubiquitous in nonequilibrium systems such as supercooled liquids, amorphous solids, active matter, and spin glasses. It is often challenging to determine if such observations are related to a true second-order phase transition as in the equilibrium case or simply a crossover and even more so to measure the associated critical exponents. Here we show that the simulation results of a hard-sphere glass in three dimensions are consistent with the recent theoretical prediction of a Gardner transition, a continuous nonequilibrium phase transition. Using a hybrid molecular simulation-machine learning approach, we obtain scaling laws for both finite-size and aging effects and determine t2021-01-01T00:00:00Z2021 Mar2025-04-05T11:54:08.51Z2022-02-11T10:16:59.963ZS-EPMC79803903383658310.1073/pnas.2017392118