Although it is commonly assumed that the physics of inflation and the subsequent (p)reheating epoch can be understood by means of simple effective field theories (e.g. due to symmetry restoration), there is no guarantee that this reductionist point of view is realized. In fact, some ultraviolet completions of inflation and reheating tend to involve many fields, with complicated interactions that can lead to significant elements of randomness in the dynamics. Nevertheless, in the limit of many fields/interactions, emergent universal properties may arise. In this talk I will present a statistical framework for characterizing non-adiabatic particle production in the early universe, namely scenarios with multiple coupled fields in a time dependent background with stochastically varying effective masses, cross couplings and intervals between interactions. I will show how the evolution of coarse-grained quantities, such as the particle occupation numbers, can be derived from a Fokker-Planck equation.