On the analysis of two-time correlation functions: equilibrium versus non-equilibrium systems.

X-ray photon correlation spectroscopy (XPCS) is a powerful tool for the investigation of dynamics covering a broad range of timescales and length scales. The two-time correlation function (TTC) is commonly used to track non-equilibrium dynamical evolution in XPCS measurements, with subsequent extraction of one-time correlations. While the theoretical foundation for the quantitative analysis of TTCs is primarily established for equilibrium systems, where key parameters such as the diffusion coefficient remain constant, non-equilibrium systems pose a unique challenge. In such systems, different projections ('cuts') of the TTC may lead to divergent results if the underlying fundamental parameters themselves are subject to temporal variations. This article explores widely used approaches for TTC calculations and common methods for extracting relevant information from correlation functions, particularly in the light of comparing dynamics in equilibrium and non-equilibrium systems.