Economic thermodynamics

Highlights

• Economic thermodynamics as a phenomenological theory is developed.

• The economic meaning of internal energy and temperature in economics is established.

• Economic thermodynamics allows a natural description of inflation.

• The thermodynamic conditions of market equilibrium stability are derived.

• Le Chatelier’s principle is considered as applied to economic systems.

Abstract

A thermodynamic approach to the description of economic systems and processes is developed. It is shown that there is a deep analogy between the parameters of thermodynamic and economic systems (markets); so each thermodynamic parameter can be associated with a certain economic parameter or indicator. The economic meaning of such primordially thermodynamic concepts as internal energy and temperature has been established. It is shown that many economic laws, which in economic theory are a generalization of the results of observations, or are based on the analysis of the psychology of the behavior of market actors, within the framework of economic thermodynamics can be obtained as the natural and formal results of the theory. In particular, we show that economic thermodynamics allows a natural description of such a phenomenon as inflation. The thermodynamic conditions of market equilibrium stability are derived and analyzed, as well as the Le Chatelier’s principle as applied to economic systems.

Introduction

In recent decades, the understanding has come that the methods and theories developed in relation to physical systems can be successfully used to description of the systems outside physics, consisting of a large number of interacting elements. In such systems, specific mechanisms of interaction of elements become secondary, while certain collective properties come to the fore, which do not depend on the nature of the system, and should be the same for both physical and non-physical systems. It is these collective properties that determine the behavior of such systems as a whole.

An example of this is the application of the methods of thermodynamics and thermostatistics to the description of economic systems and processes, despite the fact that economics, as a theory, is fundamentally different from theories in physics, primarily in terms of its structure and principles of construction [1].

The methods of thermodynamics and thermostatistics as applied to the description of economic systems and processes were considered in papers [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21]. So in works [2], [3], [9], [10], [11], [17], [19], [20], analogs of the first and second laws of thermodynamics are introduced and analyzed in relation to economic systems. The economic analog of the Carnot cycle is considered in works [2], [3], [7], [8], [9], [10], [11]. In works [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [19], [20], a new (for economics) quantitative indicator, temperature, is introduced and its economic meaning is discussed. The law of increasing entropy as applied to economic processes was apparently first discussed in [18]. In works [2], [3], [4], [5], [6], [9], [12], [13], [15], [16], [17], [20], various economic systems and processes are analyzed by methods of statistical physics and the connection of economic temperature with probability distributions of wealth and income has been shown.

At the same time, it should be noted that in the cited works, thermodynamic methods and thermodynamic terminology were often used intuitively and formally, at the level of external analogies, without strict theoretical justification.

In work [19], we have shown that thermodynamics of markets can be constructed as a phenomenological theory, by analogy with how it is done in physics.

In particular, proceeding from general principles, we showed [19] that the market for a certain goods is described by the equation

$$\delta Q=dE+pdV-\mu dN$$

which, both in form and in content, is analogous to the first law of thermodynamics, where $E$ is the amount of money available in the system (internal energy of system), $V$ is the amount of goods in the system (volume of the system), $p$ is mean price of goods in the system (pressure), $N$ is the number of elements (market actors), $\mu$ is the financial potential — a change in the amount of money in the system when the number of its elements changes per unit (due to migration, dissociation, recombination, etc.), $\delta Q$ is the heat — the amount of money that the elements of one system directly transfer to the elements of another system without buying and selling goods (for example, direct investments, dividend payments, cash gifts, donations, taxes, subsidies, loans, loan payments, etc.) and without changing the number of elements in the system.

The first law (1) shows that there are three ways to change the energy of an economic system [19]: (i) by changing the volume of the system (work); (ii) by changing the number of system elements (financial work); (iii) without changing the volume of the system and the number of its elements due to the direct transfer of money between the elements (heat transfer or heat exchange). There are no other ways to change the energy (the amount of money) of the economic system.

It was shown in [19] that for economic systems, the entropy S can be introduced in a natural way, which for nonequilibrium processes satisfies the condition (second law)

$$dS\ge \delta Q/T$$

where $T$ is the temperature of the economic system (economic temperature) — an intensive parameter that characterizes the economic system as a whole.

For equilibrium (quasi-static) processes, the entropy

$$S^0=S^0\left(T,V,N\right)$$

satisfies the equation (second law for equilibrium processes)

$$d{S}^0=\delta Q/T$$

As in physics, the parameters $(p,T,V,N,E)$ of the economic system are not independent, but are related by relations (equations of state) that characterize the given economic system [19].

These include the thermal equation of state of the economic system

$$p=f(T,V,N)$$

and the energy (financial) equation of state of the economic system

$$E=E(T,V,N)$$

which can be obtained by methods of economic thermostatistics [19].

In particular, for a primitive (ideal) market [19], the equation of state (5) has the form

$$pV=k_{0}NT$$

where $k_0$ is the numerical constant that determines the scale of temperature [19] — an analog of the Boltzmann constant.

Despite the fact that economic temperature, as an indicator of the state of the economic system, was introduced and discussed in many works (see, for example, [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [19], [20]), its real physical meaning and measurement methods remain unclear.

This paper is a further development of the ideas of the paper [19]. In particular, we will clarify the concepts of energy and temperature of an economic system, consider the thermodynamic conditions for the stability of the equilibrium of economic systems, and show the possibilities of thermodynamic methods in describing some economic processes.