Heat capacity in bits

by P. Fraundorf, UM-StL Physics & Astronomy

An active revision of cond-mat/9711074 in the Los Alamos archives


Statistical physics since Shannon has shown, following the 19th century work of Gibbs, that physical units for temperature kT defined statistically (via 1/T = dS/dE) are energy per ``nat'' of information uncertainty. Consequences of this for heat capacities are explored here for quadratic systems, and systems for which equipartition has little meaning. We show for any system that total thermal energy E over kT (an integral or average heat capacity when T>0) is the log-log derivative of multiplicity with respect to energy, as well as (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. Similarly the work-free instantaneous heat capacity C_v/k is a ``local version'' of this log-log derivative equal (for example) to bits of information lost per 2-fold increase in temperature. This makes C_v/k independent of both: (i) the energy zero, unlike E/kT, and (ii) one's choice of the Lagrange multiplier for energy (e.g. kT versus 1/kT) to within a constant, explaining why it's usefulness may go well beyond the detection of phase changes and quadratic modes. From UMStL-CME-94a09pf.

July 2002 PDF version of the paper, with color figures reorganized and (thanks to RevTeX4) incorporated directly into the text.