When a system is brought to a critical phase transition, such as the gas-liquid critical point where the density difference between liquid and gas disappears, or the Curie point of a ferromagnet where the spontaneous magnetization disappears, many of its properties exhibit singular behavior. Beginning with Johannes van der Waals's work in the 19th century,1 analyses of critical phenomena have largely focused on static properties, such as free energies, equilibrium expectation values and linear responses to timeindependent perturbations. In classical statistical mechanics, static properties are determined by the equal-time correlation functions. However, critical singularities also occur in dynamic properties, such as multi-time correlation functions, responses to time-dependent perturbations, and transport coefficients. Those properties cannot be derived from the equilibrium distribution. A different approach is needed.
Halperin, B. I. (2019). Theory of dynamic critical phenomena. Physics Today, 72(2), 42–43. https://doi.org/10.1063/PT.3.4137