shows the simulated thermal evolution of a single vial and illustrates the definition of these quantities, while Figure (b) provides complimentary information about the ice mass evolution. The solidification time of a vial, t sol , denotes the elapsed time between the nucleation event at time t nuc and the point in time when freezing is considered to be complete for this vial, denoted with t fr . The definition for such completion is to some extent arbitrary; for this work we assume solidification to be complete when m i/ m w = 0.9; however, the model is compatible with any definition based on temperature or ice mass fraction. In our prior work, we studied the effect of the threshold on the characteristic quantities, and we found that it did not affect the observed trends for values in the range of m i/ m w = 0.85 -0.95. As it is apparent from Figure (b), higher values for the endpoint should be avoided, since the amount of ice that can be formed in the vial is ultimately limited by the freezing-point depression for a given storage temperature, i.e. some water will always remain in the solution. Assuming sufficient knowledge of the specific formulation to be frozen, one could alternatively use the attainment of the glass transition temperature of the solution as indicator for completion of freezing. Indeed, there is no consensus in literature regarding the definition of complete freezing, with some authors relying on ice mass based definitions, and some relying on the glass transition temperature. We interpret the distribution of the characteristic quantities among vials as measure of batch heterogeneity: vials that nucleate and solidify differently, will presumably have different mean crystal sizes and different API activity levels, 6,25,36 even if the practical relevance of these differences cannot be known a priori. We compute these distributions by running a large number of independent simulations of the process and by determining the corresponding probability density functions f nt (t), f nT (T ) and f sol (t). By definition, f nt (t)dt provides the fraction of nucleation events that take place between t nuc and t nuc + dt; f nT (T )dT the fraction that nucleates at temperatures between T nuc and T nuc + dT ; f sol (t)dt is the fraction of freezing processes with solidification times between t sol and t sol + dt. In the same way we also define bi-and trivariate distributions of the characteristic quantities. The broadness of the simulated probability density functions is gauged in this work by the difference between the 10% and 90% quantiles of the distribution.