Critical fluctuations and slowing down of chaos
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.