Thermodynamic and dynamical predictions for bifurcations and non-equilibrium phase transitions

“Critical transitions”, in which systems switch abruptly from one state to another are ubiquitous in physical and biological systems. Such critical transitions in complex systems are commonly described as dynamical processes within the framework of nonlinear dynamics and the bifurcation theory. However, systematic treatment from the global thermodynamic perspective is still challenging. Furthermore, from the previous established dynamical framework, a universal early-warning signal for predicting such transitions is still not very clear and complete. Here we developed a non-equilibrium thermodynamic and dynamical framework for general complex systems. Our approach used the analogy to the conventional statistical mechanical treatment for the equilibrium phase transitions, while the nature of the non-equilibrium dynamics is still captured and reflected. Applying this framework to two well-known non-equilibrium systems, we found warning signals based on thermodynamic quantities and the time-reversal symmetry breaking nature of non-equilibrium systems can be detected much earlier than those explored in the previous works based on nonlinear dynamics and the bifurcation theory. Irreversibility of the observed time series strongly correlates to the behavior of these thermodynamic quantities and provides a practical way for predicting transitions. Our work provides a general yet practical approach for exploring collective behaviors in complex systems.