Relations between quenched and annealed initial conditions in relaxation

Determine the precise relations between fixed (quenched) initial conditions and random (annealed) initial conditions with respect to the relaxation problem in statistical mechanics.

Background

The paper distinguishes between fixed (quenched) and random (annealed) initial conditions as two ways of modeling uncertainty about the initial state of a deterministic dynamical system. Quenched initial conditions remain fixed during the evolution, whereas annealed descriptions average over a distribution of initial conditions.

The author notes that the relationship between these two settings and the resulting relaxation behavior has not been established. Clarifying this relationship is important because the paper’s predictive framework allows stationary and non-stationary distributions to depend on the observer’s information about the initial condition.