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

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.

5 pages, 5 figures

References in corpus (3)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Relaxation to thermal equilibrium in the self-gravitating sheet model
• Brownian regime of finite-N corrections to particle motion in the XY hamiltonian mean field model

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