I tried to understand life systems from the thermodynamic laws since I was an undergraduate student. I hope to develop a mathematical theory of life systems parallel to classical mechanics as a mathematical theory of general systems. I read about many existing theories, such as Prigogine’s theory. However, these theories do not model life processes directly. For a long time, I had little idea how to develop such a theory. I only knew that thermodynamic processes are represented by partial differential equations. So I stick to the theory of partial differential equations, hoping something will turn up some day.

It was after many years before I bumped into the Black-Scholes equation. The Black-Scholes equation was originated in financial economics. From my perspective, this equation is a mapping from lognormal processes. Lognormal processes can be understood as the representation of extracting low entropy to compensate for dissipation, which is the essence of life processes. I sensed that the Black-Scholes theory could lead me further in developing a mathematical theory of living systems.

I started to think about the Black-Scholes theory in 1995, when I was teaching mathematics in Hong Kong. In 1997, I joined an investment bank. There, I learned to associate mathematical theories with investment decisions. Abstract symbols become concrete.  A year later, I returned to academia , this time as a finance professor in Singapore. After several years, I worked out a theory of economics that provide an analytical relation among major factors in economics: such as fixed cost, variable cost, investment horizon, discount rate and uncertainty. It provides a simple and consistent understanding on broad range of problems in economic and biological systems. More detailed discussion can be found from books and papers written by me and others. 

Since human activities are mainly measured by economic values, we need to answer how thermodynamic value is related to economic value. I took a trip from Singapore to Vancouver in August, 2000. On the plane I read Shannon’s classical paper that established information theory. Soon I realized that value can be defined exactly the same way as information: the reduction of entropy. I wrote down the draft on the plane. But it took me two years before I finally wrote the paper. I shall briefly compare our theory of value with the mainstream theory of value. There are two versions of theory of value. The first one is the popular version taught in classrooms, which defines value as scarce resources. The second one is the formal version represented by Debreu’s Theory of Value, which does not provide a measurable quantity of value. The popular version and the formal version are disconnected. Our theory defines value as a function of scarcity and provides a rigorous and easy to apply mathematical theory of value. The entropy theory of value offers a unified understanding of physical entropy, information and economic value. It provides a quantitative measure of value that is highly consistent with our intuitive understanding.

Many people do not agree that theories of social sciences should be derived from physical laws. They argue that physical laws are fixed while the human mind is free. So I was driven to better understand mind. The mind of animals, just like the bodies of animals, is shaped by natural selection to best adapt to physical laws. Specifically, the mind is evolved to search for natural resources at low cost. Since entropy provides a universal measure of resources, it is inevitable that information, which we collect for our survival, is represented by the entropy function mathematically. When observing the problems of the mind from the lens of physical laws, many complex and confusing problems become simple and clear. The entropy theory of mind provides a simple and unified understanding of many patterns in human psychology and market patterns documented in the literature of behavioral finance. This shows that research on mind, just like research on matter, can be carried out in an analytical, quantitative and systematic way from the foundation of physical laws. The entropy theory of mind provides a natural theoretical foundation to understand market patterns and investor behaviors that are the focus of investigation in behavioral finance.

The theory is systematically summarized in my book, The Physical Foundation of Economics: An Analytical Thermodynamic Theory, published in 2005. Since then, I have been updating the theory and applying the theory to different fields, mainly in the area of finance.