  Information theory this century has clarified the 19th century work of Gibbs,
and has shown that natural units for temperature kT, defined via 1/T=dS/dE, are
energy per nat of information uncertainty. This means that (for any system) the
total thermal energy E over kT is the log-log derivative of multiplicity with
respect to energy, and (for all b) the number of base-b units of information
lost about the state of the system per b-fold increase in the amount of thermal
energy therein. For ``un-inverted'' (T>0) systems, E/kT is also a
temperature-averaged heat capacity, equaling ``degrees-freedom over two'' for
the quadratic case. In similar units the work-free differential heat capacity
C_v/k is a ``local version'' of this log-log derivative, equal to bits of
uncertainty gained per 2-fold increase in temperature. This makes C_v/k (unlike
E/kT) independent of the energy zero, explaining in statistical terms its
usefulness for detecting both phase changes and quadratic modes.
