Heat Capacity in Bits

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. © 2003 American Association of Physics Teachers. @DOI: 10.1119/1.1593658#