Transition functions and correlation functions in the analysis of dynamic systems

An understanding of the dynamic behavior of complex systems such as supercooled liquids requires a knowledge of the microscopic processes occurring in them. Correlation functions, which can be derived from experimental measurements of macroscopic properties or from computer simulations, cannot distinguish between particles that have never moved and those that have changed their position or state and then returned to the original one. Such a distinction can be obtained from the comparison of a correlation function with the transition function, i.e., the fraction of particles that have never moved up to time t. As the author demonstrates by an extension of his recently published results for the ferromagnetic Potts model [J. Chem. Phys. 124, 214508 (2006)], valuable insights into the microscopic behavior of a system can be obtained from such a comparison. A generalization of the transition function to a first passage function can provide useful extra insights.