  Hot-atoms reactions mechanisms bring about reaction rates which are several
orders of magnitude higher than those expected in the case of ad-atoms which
have thermalized with the surface. This paper addresses the issue of a possible
thermodynamic characterization of the adlayer under reactive conditions and at
the steady state. In turn, this implies to tackle the question of determining
the temperature of the ad-atoms. This is done by means of a nonequilibrium
statistical thermodynamic approach, by exploiting a suitable definition of the
entropy. The interplay between reaction rate, vibrational temperature of the
ad-atoms and adsorbed quantities is highlighted. It is shown that the
vibrational temperature depends on reaction rate logarithmically and exhibits a
non-linear scaling on physical quantities linked to the energetics of the
reaction, namely the adsorption energy and the binding energy of the molecule.
The present modeling is also discussed in connection with response equations of
nonequilibrium thermodynamics.

Materials Science