The joint probability distribution function of global interaction complex systems

TL;DR

This paper derives a joint probability distribution function for complex systems with long-range interactions, challenging the traditional independence assumption, and verifies it with foreign exchange trading data.

Contribution

It introduces a new joint probability distribution function for coupled complex systems that accounts for long-range interactions, extending beyond previous independent models.

Findings

The derived distribution aligns with observed foreign exchange data.

The model captures long-range interaction effects in complex systems.

Verification confirms the theory's consistency with real-world data.

Abstract

Based on the relationship that the interaction energy between any two subsystems is equal to their internal energy multiplied by the interaction coefficient, we have derived a series correlated expressions of statistical physical quantities, such as the interactional average energy, the probability distribution function of internal energy, and so on. It should be noted that the probability distribution function we obtained is existing in many complex systems involving long-range interactions. Further, based on the zeroth law of thermodynamics, we have also obtained the joint probability distribution function of two coupled complex systems. It must be note that the joint probability distribution function we obtained no longer satisfies the common independent multiplication relationship in the previous researches. Finally, we selected several representative foreign exchange high-frequency trading data for verification and found that the theory is consistent with the reality.