Relaxation time as early warning signal of avalanches in self-organizing systemsZhiqin Ma ,1 Chunhua Zeng,1,* and Wu-Ming Liu 2,3,4,† 1Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China2Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China 3School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China 4Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China (Received 9 July 2023; accepted 20 November 2023; published xxxxxxxxxx)Avalanches are sudden, destructive, and extremely difficult to forecast natural disasters that can result innumerous fatalities and extensive property damage. Given the immense danger posed by avalanches, there isa significant amount of attention paid to accurately predicting these events. We investigate the predictabilityof large avalanches in a class of self-organizing systems, which change their internal structure or function inresponse to external circumstances by manipulating or organizing other elements of the same system. Here, wepropose a practical relaxation time to replace a traditional recovery time, and importantly, the relaxation timedoes not require the removal of part of the resources (perturb state variables) in the environment. This workprovides examples of the forest fire model and sandpile model as self-organizing systems in which the relaxationtime successfully predicts the onset of large avalanches. Furthermore, the relaxation time can show a consistentwith the increasing trend in both oscillatory and nonoscillatory bifurcations, suggesting that the relaxation timeis more universal than traditional indirect metrics such as the variance and the lag-1 autocorrelation function. Weaim to identify early warning signals before the onset of large avalanches and provide scientific evidence andsignificant information for managers to formulate mitigation countermeasures and strategic decisions.DOI: 10.1103/PhysRevResearch.00.003000