I enjoyed reading the article An economic analogy to thermodynamics by Wayne Saslow. It proposes mapping different economic variables to thermodynamic ones. It learnt a little about economics which was nice. He suggests the following analogies between thermodynamic and economic variables. Wealth, utility, surplus, price, and number of goods, correspond to free energy, internal energy, TS, chemical potential, and particle number respectively. The Maxwell relations correspond to what in economics are known as Slutsky conditions!
The economic temperature T is identified with the level of economic development.
Economic entropy is expected to be related to "economic variety, which in turn may be a measure of the economic value of leisure."
Here is a small extract to give you the flavour. It considers the application of the analogue of the Gibbs-Duhem relation Ndmu = -SdT + VdP
I did not think the papers review of thermodynamic concepts was particularly insightful. But, that is what I think about most textbooks. I think the following two points may be particularly relevant for economic analogues.
First, the zeroth law tells us that there is a single variable that tells us whether or not two systems will change when they are brought into thermal contact. This allows us to define temperature. So does there exist a single economic variable that will tell us whether two isolated economic systems will change when they are allowed to interact (e.g., two countries start trading with one another)?
Second, entropy is all about irreversibility. It tells us when the system is isolated whether or not we can get from one equilibrium state to another. Economic systems do undergo irreversible changes. Is there a single variable that can describe the ordering of economic equilibrium states?