Metrics and Energy Landscapes in Irreversible Thermodynamics

We describe how several metrics are possible in thermodynamic state space but that only one, Weinhold’s, has achieved widespread use. Lengths calculated based on this metric have been used to bound dissipation in finite-time (irreversible) processes be they continuous or discrete, and described in the energy picture or the entropy picture. Examples are provided from thermodynamics of heat conversion processes as well as chemical reactions. Even losses in economics can be bounded using a thermodynamic type metric. An essential foundation for the metric is a complete equation of state including all extensive variables of the system; examples are given. Finally, the second law of thermodynamics imposes convexity on any equation of state, be it analytical or empirical.