# Self-averaging fluctuations in the chaoticity of simple fluids

## TL;DR

This paper investigates how intermolecular forces influence dynamical fluctuations in simple fluids, revealing that the first Lyapunov exponent exhibits weak self-averaging affected by force range, while the Kolmogorov-Sinai entropy fluctuations diverge.

## Contribution

It demonstrates the differential impact of attractive and repulsive forces on the self-averaging properties of Lyapunov exponents in fluids.

## Key findings

- First Lyapunov exponent self-averages weakly, depending on force range.
- Kolmogorov-Sinai entropy fluctuations diverge with system size.
- Fluctuations obey fluctuation-dissipation relationships.

## Abstract

Bulk properties of equilibrium liquids are a manifestation of intermolecular forces. Here, we show how these forces imprint on dynamical fluctuations in the Lyapunov exponents for simple fluids with and without attractive forces. While the bulk of the spectrum is strongly self-averaging, the first Lyapunov exponent self-averages only weakly and at a rate that depends on the length scale of the intermolecular forces; short-range repulsive forces quantitatively dominate longer range attractive forces, which act as a weak perturbation that slows the convergence to the thermodynamic limit. Regardless of intermolecular forces, the fluctuations in the Kolmogorov-Sinai entropy rate diverge, as one expects for an extensive quantity, and the spontaneous fluctuations of these dynamical observables obey fluctuation-dissipation like relationships. Together, these results are a representation of the van der Waals picture of fluids and another lens through which we can view the liquid state.