The internal energy expression of a long-range interaction complex system and its statistical physical properties

TL;DR

This paper derives an internal energy expression for complex systems with long-range interactions, explores their statistical properties, and highlights the dependence on interaction strength and particle number.

Contribution

It introduces a new internal energy formula for long-range interaction systems and analyzes their statistical physical properties based on microstate probabilities.

Findings

Properties depend strongly on interaction coefficient

System behavior varies with particle number

Derived probability distribution function for microstates

Abstract

Considering the interactions of two arbitrary particles, we obtain an internal energy expression of the complex system having long-range interactions. Based on the postulate of "equal-probability principle" for all microstates, the probability distribution function of the system is derived, and consequently, some main statistical physical properties of the system are revealed. It is important to find that the properties of a long-range interaction system are very closely dependent on the interaction coefficient and particle number.