  This work represents the first chapter of a project on the foundations of
first-principle calculations of the electron transport in crystals at finite
temperatures. We are interested in the range of temperatures, where most
electronic components operate, that is, room temperature and above. The aim is
a predictive first-principle formalism that combines ab-initio molecular
dynamics and a finite-temperature Kubo-formula for homogeneous thermodynamic
phases. The input for this formula is the ergodic dynamical system
$(\Omega,\mathbb G,{\rm d}\mathbb P)$ defining the crystalline phase, where
$\Omega$ is the configuration space for the atomic degrees of freedom, $\mathbb
G$ is the space group acting on $\Omega$ and ${\rm d}\mathbb P$ is the ergodic
Gibbs measure relative to the $\mathbb G$-action. The present work develops an
algorithmic method for quantifying $(\Omega,\mathbb G,{\rm d}\mathbb P)$ from
first principles. Using the silicon crystal as a working example, we find the
Gibbs measure to be extremely well characterized by a multivariate normal
distribution, which can be quantified using a small number of parameters. The
latter are computed at various temperatures and communicated in the form of a
table. Using this table, one can generate large and accurate
thermally-disordered atomic configurations to serve, for example, as input for
subsequent simulations of the electronic degrees of freedom.
