Abstract
Abstract
Thermal macroeconomics (TM) applies the axiomatic structure of classical thermodynamics to exchange economies, predicting that each economy admits an entropy function of state that governs macroscopic behaviour under contact. The possibility of such a macroscopic reduction is a fundamental result in physics, where it underlies the thermodynamic description of many complex systems. With analogous assumptions, the same mathematics leads to the same conclusion in economics. Previous tests of the framework have focussed primarily on bilateral exchange models in which agents meet pairwise and the outcome of exchanges is chosen from a probability distribution based on utility functions for the agents. We extend the study to order-book economies, where exchange is mediated through a centralised exchange using quoted prices and order-matching rather than pairwise redistribution. The resulting dynamics are not easy to analyse and it is not even clear that the axioms for thermal macroeconomics hold, so we test thermodynamic behaviour empirically. Using a measurement technique that is economically analogous to calorimetry, we show that intensive variables can be measured, and they yield an integrable entropy surface. On the other hand, under full contact of two order-book economies, where both money and goods may flow between books, cross-book trading is dominated by price arbitrage rather than wealth distribution, and the books converge to a common midprice rather than to maximum entropy. Nonetheless, under financial contact between two order-books using an affiliate-based settlement mechanism, the standard thermodynamic prediction of temperature equalisation is recovered.