Equilibrium economics with a two-strata social structure

Abstract

According to Adam Smith, equilibrium economics essentially satisfies UD-statistics [1] when the interaction between individual players involved in the economic process are not taken into account.After the work of Irving Fisher, who formulated the main law of economics as an analog of the Claiperon-Clausius-Mendeleev relation corresponding to the Boltzmann-Maxwell ideal gas, the authors have developed this approach on the basis of the general principles of UD-statistics by assigning to the nominal interest rate the role of the chemical potential μ (with a minus sign).The extremely important notion of the number of degrees of freedom was introduced as a parameter describing ethical principles and traditions, which allow to preserve not only human society, but also certain intuitively acquired rules and regulations imprinted in the individual memory of each player in the economic process.Further, as a purely mathematical consequence of the properties of the notion of "anti-money" (debts), certain limiting points of the UD-statistics were derived; they allow to determine at least intervals [2] of parameters within which catastrophes, such as defaults, are possible.In thermodynamics, as a rule, metastable states are neglected. Now negative pressure is a metastable state. But the system can remain in such states not too near to the spinodal for millions of years. Since negative pressures correspond to negative energies, and negative energies, to anti-particles, it follows from Irving Fisher's correspondence principle (according to which the number of particles corresponds to the total amount of money) that negative pressures correspond to debts. And a developing economy cannot do without debts.Therefore, the theory of metastable states must, undoubtedly, be investigated very closely if we wish to establish the correspondence principles between economics and thermodynamics.In our previous work, we described this analogy for subcritical states and compared the phase transitions with revolutions, defaults, and other sharp changes in the economy (see, in particular,The interaction in question used in [5] has both an attractive component and a repulsive one. This is similar to the interaction between players involved in economic processes. Competition leads to repulsion. The advantages of uniting result in attraction. If we consider two agents, it is easy to see both processes at work.In supercritical thermodynamics, there are no phase transitions, but, instead, it follows from the consideration of interaction that the supercritical structure splits into two practically noninteracting parts: the mesoscopic system (consisting of clusters) and the microscopic one (consisting of the monomers that form the gas). This splitting is essentially caused by particle interaction.As in statistical physics, it is natural to consider just pairwise interactions. This yields the simplest and most adequate model.