  The laws of thermodynamics provide a clear concept of the temperature for an
equilibrium system in the continuum limit. Meanwhile, the equipartition theorem
allows one to make a connection between the ensemble average of the kinetic
energy and the uniform temperature. When a system or its environment is far
from equilibrium, however, such an association does not necessarily apply. In
small systems, the regression hypothesis may not even apply. Herein, we show
that in small nonequilibrium systems, the regression hypothesis still holds
though with a generalized definition of the temperature. The latter must now be
defined for each such manifestation.
