Analysis of the particle transfer between two systems under unification

TL;DR

This paper analyzes how two systems of different dimensions unify, focusing on particle transfer, and provides explicit formulas for system parameters, entropy, and conditions for zero transfer, relevant to physics and economics.

Contribution

It introduces explicit formulas for the temperature, dimension, and particle transfer during the unification of two systems with different dimensions.

Findings

Derived formulas for temperature and dimension of the united system.

Explicit expression for the number of particles transferred.

Identified conditions for zero particle transfer regime.

Abstract

We investigate unification of two systems of identical elements having different dimensions which may be of interest for both physics and economics. Characteristic parameters as well as explicit formulae for the temperature (in economics - capital turnover) and dimension of the united system are obtained as functions of parameters of the initial systems. Expressions also found for the entropies of initial and united system. The process of unification is accompanied by the transfer of particles (money) between the systems and explicit expression is obtained for the transferred number of particles (size of the capital). A relation between parameters of the initial systems also found which defines the regime with zero particle transfer.