  Ultrafast laser radiation or beams of fast charged particles primarily excite
the electronic system of a solid driving the target transiently out of thermal
equilibrium. Apart from the nonequilibrium between the electrons and atoms,
each subsystem may be far from equilibrium. From the first principles, we
derive the definition of various atomic temperatures applicable to
electronically excited ensembles. It is shown that the definition of the
kinetic temperature of atoms in the momentum subspace is unaffected by the
excitation of the electronic system. When the electronic temperature differs
from the atomic one, an expression for the configurational atomic temperature
is proposed, applicable to the electronic-temperature-dependent interatomic
potentials (such as ab-initio molecular dynamics simulations). We study how the
configurational temperature behaves during nonthermal phase transition,
triggered by the evolution of the interatomic potential due to the electronic
excitation. It is revealed that upon the ultrafast irradiation, the atomic
system of a solid exists temporarily in a multi-temperature state: separate
equilibria in the momentum and configurational subspaces. Complete
equilibration between the various atomic temperatures takes place at longer
timescales, forming the energy equipartition. Based on these results, we
propose a formulation of multi-temperature heat transport equations.
