I emphasize that the ideas, concepts and principles of classical economic theory constitute the foundation of physical economics in my understanding, and the approaches and methods of theoretical physics play here the role of the second plan. The task of these theoretical instruments is to give the adequate mathematical description of these ideas, concepts and principles. These help create the formal framework of the theory, as well as develop mathematical apparatus for describing the structure and behavior of market economies. Why is this possible? The point is that, in structure and properties, the many-agent market economic systems are quite similar to the many-particle physical systems. Take, for example, the polyatomic molecules. Indeed:
1. Markets consist of agents. Molecules consist of atoms.
2. Agents interact between themselves. Atoms interact between themselves.
3. Everything that markets do, the interacting agents do. Everything that molecules do, the interacting atoms do.
4. Dynamics of markets are determined by a principle of maximization (e.g. the trade maximization principle). Dynamics of molecules is determined by a principle of maximization (e.g. the least action principle).
5. Uncertainty and probability is an inherent important property of the market behavior. The same is valid for dynamics of molecules.
And this is still far from a complete enumeration of coincidences and analogies between the economic and physical systems.
It is widely-known that presently, advanced mathematical methods are applied in describing the dynamics of complex economic systems much less frequently than in physics. As far as the difference in the level of the penetration of formal mathematical methods into economics and physics is concerned, it is possible with reasonable caution to assert that this difference does not lie in the fact that in principle, mathematics cannot be widely used in economics by its very nature. Instead, physics has proven to be the more developed science mathematically in modern times for a variety of historical and technological reasons. This has been the situation for the past 300 years. Beautiful mathematical models have been created in physics during this time frame to describe dynamic phenomena in many-particle systems. Unfortunately, the same cannot be said for economic theory. It is obvious to me that, things being as they are, the correct conclusion for us now must not be to preserve the