The temperature 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 to is the multiplicity exponent (log–log derivative of the multiplicity) with respect to energy, as well as the number of base- units of mutual information that is lost about the state of the system per -fold increase in the thermal energy. Similarly, the no-work heat capacity is the multiplicity exponent for temperature, making independent of the choice of the intensive parameter associated with energy (for example, vs to within a constant, and explaining why its usefulness may go beyond the detection of thermodynamic phase changes and quadratic modes.
Topics
Thermodynamic properties
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