Critical fluctuations and slowing down of chaos

TL;DR

This paper investigates the critical slowing down of chaos near the liquid-vapor critical point, revealing how structural correlations stabilize fluids against chaos through analysis of Lyapunov modes and critical dynamics.

Contribution

It introduces a novel coupling of nonlinear dynamics and statistical physics to analyze the emergence of critical fluctuations and chaos suppression in fluids at the critical point.

Findings

Unstable Lyapunov modes soften near the critical point

Characteristic exponents of modes are suppressed, indicating reduced sensitivity to initial conditions

Finite-time fluctuations show diverging timescales and power-law behavior

Abstract

Fluids cooled to the liquid-vapor critical point develop system-spanning fluctuations in density that transform their visual appearance. Despite the rich phenomenology of this critical point, there is not currently an explanation of the underlying mechanical instability. How do structural correlations in molecular positions overcome the destabilizing force of deterministic chaos in the molecular dynamics? Here, we couple techniques from nonlinear dynamics and statistical physics to analyze the emergence of this singular state. Our numerical simulations reveal that the ordering mechanisms of critical dynamics are directly measurable through the hierarchy of spatiotemporal Lyapunov modes. A subset of unstable modes softens near the critical point, with a marked suppression in their characteristic exponents reflecting a weakened sensitivity to initial conditions. Finite-time fluctuations in these exponents, however, exhibit diverging dynamical timescales and power law signatures of critical dynamics. Collectively, these results are symptomatic of a critical slowing down of chaos that sits at the root of our statistical understanding of the singular thermodynamic responses at the liquid-vapor critical point.