Heat capacity in bits

Details Heat capacity in bits Heat capacity in bits

1997-11-10

arxiv.org/abs/cond-mat/9711074v2

Amer. J. Phys. 71 (11) 1142-1151 (November 2003)

Physics

Condensed Matter

Statistical Mechanics

7 pages (3 figs, 16 refs) RevTeX; clarify, new plots; comments http://www.umsl.edu/~fraundor/cm971174.html

Scientific paper

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.

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