  In this work we show that the standard method to obtain nucleation
rate-predictions with the aid of atomistic Monte-Carlo simulations leads to
nucleation rate predictions that deviate $3-5$ orders of magnitude from the
recent brute-force molecular dynamics simulations [J. Diemand, R. Ang\'{e}lil,
K. K. Tanaka, and H. Tanaka, J. Chem. Phys. \textbf{139}, 074309 (2013)]
conducted in the experimental accessible supersaturation regime for
Lennard-Jones argon. We argue that this is due to the truncated state space
literature mostly relies on, where the number of atoms in a nucleus is
considered the only relevant order parameter. We here formulate the
nonequilibrium statistical mechanics of nucleation in an extended state space,
where the internal energy and momentum of the nuclei is additionally
incorporated. We show that the extended model explains the lack in agreement
between the molecular dynamics simulations by Diemand et al.\ and the truncated
state space. We demonstrate additional benefits of using the extended state
space; in particular, the definition of a nucleus temperature arrises very
naturally and can be shown without further approximation to obey the
fluctuation law of McGraw and Laviolette. In addition, we illustrate that our
theory conveniently allows to extend existing theories to richer sets of order
parameters.
