Strange Scaling and Temporal Evolution of Finite-Size Fluctuation in Thermal Equilibrium

TL;DR

This paper investigates unusual scaling behaviors and temporal changes in finite-size fluctuations in a long-range interacting system at thermal equilibrium, linking them to Casimir invariants and their finite-size effects.

Contribution

It introduces a novel explanation for strange scaling and fluctuation evolution based on Casimir invariants in long-range systems, supported by numerical evidence.

Findings

Identification of strange scaling behavior in finite-size fluctuations

Demonstration of temporal evolution of fluctuations in thermal equilibrium

Linking phenomena to Casimir invariants and Vlasov dynamics

Abstract

We numerically exhibit strange scaling and temporal evolution of finite-size fluctuation in thermal equilibrium of a simple long-range interacting system. These phenomena are explained from the view point of existence of the Casimirs and their nonexactness in finite-size systems, where the Casimirs are invariants in the Vlasov dynamics describing the long-range systems in the limit of large population. This explanation expects appearance of the reported phenomena in a wide class of isolated long-range systems. The scaling theory is also discussed as an application of the strange scaling.