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# A Study of Equilibrium in a Nano-Economy

Garvin Boyle

The concept of equilibrium, as developed in the latter half of the 19th century, has played a key role in modern economic theory. However, much progress has been made recently in the study of equilibria and systems that operate far from equilibrium. To anyone who has followed recent developments in the study of dynamic systems, it is clear that an economy is a complex adaptive evolving system operating far from equilibrium. I believe that it is time for biophysical economists to re-examine the nature and role of equilibria in the context of the dynamic operation of an economy, and to develop a modern theory of economic equilibria. In this presentation I will explore the nature of one kind of economic equilibrium using a nano-economy. I will start with a brief definition of a nano-economy, and a brief description of a remarkable class of nano-economic models. These models demonstrate the same equilibrium-seeking dynamics that are also operating in the major free economies of the modern world. From there we will explore some aspects of the kind of equilibrium found in such nano-economies, with a particular focus on the equilibrium-seeking role of entropy. Starting with a definition of the current state of the model, we will expand that to a definition of key variables, and a mathematical representation of the space of all possible states as we vary the total capital in the model. We will then explore the boundaries of the aggregated state space and the relative density of states within various parts of the state space, linking these ideas to concepts in physics. We will finish with a discussion of equilibrium in this system, and the dynamic behaviour of the model as it seeks equilibrium.