Second-order Phase Transition Behavior behind Polymer Glass Transition

Glass transition has similarity to the second-order phase transition in temperature dependent changes in entropy, non-Arrhenius viscosity, and heat capacity of glass forming materials. However, it has primarily been considered to be not phase transition. Recent single-molecule spectroscopy developments prompted re-investigating glass transition at the nanometer scale probing resolution, showing that glass transition includes phenomena similar to the second-order phase transition. They are characterized by microscopic collective polymer motion and discontinuous changes in temperature dependent relaxation times, the latter of which resembles the critical slowing down of second-order phase transitions, within a temperature window above the polymer calorimetric glass transition temperature. Simultaneous collective motion and critical slowing down occurrences disclose that the second-order phase transition hides behind polymer glass transition.

Second-order Phase Transition Behavior in a Polymer above the Glass Transition Temperature

<p>Glass transition was primarily considered to be not phase transition; however, it has similarity to the second-order phase transition. Recent single-molecule spectroscopy developments have prompted re-investigating glass transition at the microscopic scale, revealing that glass transition includes phenomena similar to second-order phase transition. They are characterized by microscopic collective polymer motion and discontinuous changes in temperature dependent relaxation times, later of which is similar to critical slowing down, within a temperature window that includes the polymer calorimetric glass transition temperature. Considering that collective motion and critical slowing down are accompaniments to critical phenomena, second-order phase transition behavior was identified in polymer glass transition.</p>

Early-Warning Signals of Drought-Flood State Transition over the Dongting Lake Basin Based on the Critical Slowing Down Theory

In this study, the standardized precipitation index (SPI) data in Hunan Province from 1961 to 2020 is adopted. Based on the critical slowing down theory, the moving t-test is firstly used to determine the time of drought-flood state transition in the Dongting Lake basin. Afterwards, by means of the variance and autocorrelation coefficient that characterize the phenomenon of critical slowing down, the early-warning signals indicating the drought-flood state in the Dongting Lake basin are explored. The results show that an obvious drought-to-flood (flood-to-drought) event occurred around 1993 (2003) in the Dongting Lake basin in recent 60 years. The critical slowing down phenomena of the increases in the variance and autocorrelation coefficient, which are detected 5–10 years in advance, can be considered as early-warning signals indicating the drought-flood state transition. Through the studies on the drought-flood state and related early-warning signals for the Dongting Lake basin, the reliabilities of the variance and autocorrelation coefficient-based early-warning signals for abrupt changes are demonstrated. It is expected that the wide application of this method could provide important scientific and technological support for disaster prevention and mitigation in the Dongting Lake basin, and even in the middle and lower reaches of the Yangtze River.

Overlapping Time Scales Obscure Early Warning Signals for the Second COVID-19 Wave

Early warning indicators based on critical slowing down have been suggested as a model-independent and low-cost tool to anticipate the (re)emergence of infectious diseases. We studied whether such indicators could reliably have anticipated the second COVID-19 wave in European countries. Contrary to theoretical predictions, we found that characteristic early warning indicators generally decreased rather than increased prior to the second wave. A model explains this unexpected finding as a result of transient dynamics and the multiple time scales of relaxation during a non-stationary epidemic. Particularly, if an epidemic that seems initially contained after a first wave does not fully settle to its new quasi-equilibrium prior to changing circumstances or conditions that force a second wave, then indicators will show a decreasing rather than an increasing trend as a result of the persistent transient trajectory of the first wave. Our simulations show that this lack of time scale separation was to be expected during the second European epidemic wave of COVID-19. Overall, our results emphasize that the theory of critical slowing down applies only when the external forcing of the system across a critical point is slow relative to the internal system dynamics.