B. heat capacity in bits

Abstract: The temperature T may be expressed as the rate of energy increase per unit increase in the state uncertainty under no-work conditions. The consequences of such a choice for heat capacities are explored. I show that the ratio of the total thermal energy E to kT is the multiplicity exponent (log–log derivative of the multiplicity) with respect to energy, as well as the number of base-b units of mutual information that is lost about the state of the system per b-fold increase in the thermal energy. Similarly, the no-work heat capacity CV is the multiplicity exponent for temperature, making CV independent of the choice of the intensive parameter associated with energy (for example, kT vs 1/kT) to within a constant, and explaining why its usefulness may go beyond the detection of thermodynamic phase changes and quadratic modes.

Introductory physics supplement and slides on gambling theory & temperature.

The figure at right is a temperature scale including the full range of 1/kT in SI-units.