Maximal entropy multivariate analysis

A methodology is developed for the analysis of multivariate data by maximal entropy and it is shown how the surprisal reduces to the more familiar bivariate and univariate forms. When multivariate data is available it is shown how the uni- or bi-variate surprisal parameters can be expressed as a sum of terms containing contributions of different pathways. But if averaging so as to reduce the number of variables is performed before the data analysis then all that one can determine is the sum but not the individual contributions: averaging completely hides essential details and correlations. The formalism is illustrated by an application to ultrafast translational equilibration that occurs when a cold rare gas cluster impacts a hard surface at a hypersonic speed.