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 status quo. Nor should economists urgently develop their own unique mathematical calculations to describe economic phenomena, independent of physics. After all, why re-invent the wheel? All that is needed is to make use of some of the most salient and staggering achievements of humanity at the present time by borrowing from theoretical physics. These can be put to use for the good of the development of economic science and the global economy. This book is one of the many steps in the right direction along the proper road. Hopefully I am not wrong, although there is always that chance. There is no doubt that it will be a long road to this accomplishment, and most certainly not a fast one.

I am well aware that the very idea of using methods of theoretical physics, especially quantum mechanics, for describing economic phenomena must cause a healthy dose of skepticism from the physicists. Therefore, I emphasize that the discussion deals with the fact that only the mathematic framework of theoretical models of the respective physical systems are transferred to the physical economic models.

I incorporate into economics only the formal structural aspects of physical theories. First of all are the equations of motion for the many-particle systems, which just by themselves must not be too rigidly attached to real physical microscopic objects. Equations – they are just equations and nothing more, and if they are a beneficial descriptive tool in another science, why not make use of them? I repeat that this is just a useful mathematical object which can and should be used as a theoretical tool where it can provide benefit. For instance, in quantum mechanics wave functions and the Schrödinger equations have been successfully used for the incorporation of the uncertainty and probability principle into physics. Why, then, can we not then apply the same mathematical apparatus to the analogous uncertainty and probability principle in economic theory for purposes of mathematical description?

It is obvious that this is only an initial approximation to reality. But we are talking about modeling economic systems, and models are only models, giving only an approximate shape to the object being modeled. My physical models of economic systems also do not pretend that they are complete and precise; they can give only the approximate patterns of our market economic world, only the specific stage in our understanding of the real economic world transposed into the language of mathematics. A physical economic model is nothing other than a certain ideal, imagined construction, aimed at explaining one or more aspects of the studied phenomenon. The question is not whether it is correct or not, but whether it is useful in helping to reach a true understanding of the real economic world. Nothing more. I think that by means of this approach, some insight into the important market economy phenomena has been gained in this study.

Ten years ago I published the small book “Physical Modeling of Economic Systems: The Classical and Quantum Economies” [4]. It was my first attempt to develop an economic theory ab initio, and constructed an axiomatic basis of the theory from a limited set of first principles. The basic hallmarks of the theory that made it probabilistic and quantitative are as follows.

First. A careful, step-by-step development of the market agent-based physical economic models, where market agents play a main role in market phenomena.

Second. The complete integration of uncertainty and probability perspectives throughout the theory.

Third. A unifying, analytic framework that uses equations of motion in the formal price economic space to describe economy evolution in time.

For the last ten years, I have continually strived to advance the theory and to make it more clear and justified. In particular, for this purpose I developed the special mathematical apparatus, which is referred to in the book as probability economics. Still, I considerably advanced the theory by means of taking into consideration quantities of market goods as independent variables along with their prices. Due to this innovation, the economic price space was expanded up to the economic price-quantity space. During this time I also developed mathematical apparatus for describing the many-good, many-agent market economies. Despite the fact that achievements and expansions of theory mentioned above are very substantial, my new book carries the title “Probabilistic Economic Theory” and is, in essence, the second extended edition of my first book, in which I presented only very beginnings of the method of the agent-based physical modeling of economic systems and the basics of probabilistic economic theory.

In this book, the fundamental concepts of economic theory are exposed to critical rethinking for the purpose of answering such eternal questions of economic theory such as those regarding supply and demand, as well as market price and market force, market process and market equilibrium, invisible hand of market etc. I look at how all these concepts should be incorporated into economic theory and conveyed quantitatively in the same language in which physicists, chemists and other professionals in the so-called natural sciences present their theories, i.e., in the language of mathematics. In the book I presented maximally simplified models, in which only the most important special features and details of work of markets are described by means of maximally simplified mathematical apparatus. Let us stress here that the main aim of such basic models is only to reveal the essence of the studied phenomenon, not more. After this is accomplished, we can then develop the models further, including other, more sophisticated effects within them. This is the only true way of modeling science. Therefore, Chapters I–VIII are easily understood by first-year economics students. But the subsequent Chapters IX and X require an existing, thorough knowledge of physics, somewhere around the level of upper year physics courses. They only need have the slightest grasp of economic phenomena and laws of human action in the market economy, obtained, for example, in the course of reading the first chapters of this book. Generally, this book can be considered as an introduction into economics, written for physicists in standard physics terminology. The book, by the way, was initially taught as a set of lectures on economics for physics department students. If, after reading this book, a physics student has the impression that the presented physical economic models are quite simple and understandable, then I have solved a personal challenge. Indeed, I feel that the more complex the studied systems are and the phenomena within them, the simpler the model must be, taking into consideration only those effects which are of prime importance for describing the studied phenomena.