Critical fluctuations and slowing down of chaos

Abstract

Fluids cooled to the liquid–vapor critical point develop system-spanning fluctuations in density that transform their visual appearance. Despite a rich phenomenology, however, there is not currently an explanation of the mechanical instability in the molecular motion at this critical point. Here, we couple techniques from nonlinear dynamics and statistical physics to analyze the emergence of this singular state. Numerical simulations and analytical models show how the ordering mechanisms of critical dynamics are measurable through the hierarchy of spatiotemporal Lyapunov vectors. A subset of unstable vectors soften near the critical point, with a marked suppression in their characteristic exponents that reflects a weakened sensitivity to initial conditions. Finite-time fluctuations in these exponents exhibit sharply peaked dynamical timescales and power law signatures of the 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 liquid–vapor critical point.

Many-body chaos and anomalous diffusion across thermal phase transitions in two dimensions

“…Also, there have been similar studies in other dynamical models like Burgers hydrodynamics [17], and in the classical limit of a relativistic field theory [18]. There are many earlier studies of maximum Lyapunov exponent as well as full Lyapunov spectrum in spin models, molecular systems, and across classical phase transitions [19][20][21][22][23][24][25][26][27][28][29][30]. The conventional Lyapunov spectrum analysis, in principle, can reveal the spatiotemporal structure of chaos [31][32][33].…”

Local Shape of the Vapor–Liquid Critical Point on the Thermodynamic Surface and the van der Waals Equation of State

“…It is worth mentioning that, in contrast to the realistic experiments which seem hard to measure these two response functions near the critical point, the computer simulations are more feasible [8][9][10][11], which shows that the critical slowing down is really an overall phenomenon no matter what path is chosen to approach the critical point.…”

“…We note two seemly independent developments/facts. One is that the critical slowing down is its pathindependence [8][9][10][11][12], which means that starting from any thermodynamic state in the vicinity of a critical point to approaching it, the system has inherently slow timescales whatever thermodynamic processes are chosen. The second is that a geometrical description of a local point on a curved surface is irrespective of either the parameters chosen to label the point on the surface or the paths selected to approach it.…”

“…This paper is organized as follows. In Section 2, we prove a theorem stating that the local shape of the vapor-liquid critical point on the thermodynamic surface can never be an elliptic point, and in order to completely characterize the local shape of the critical point, we need two more response functions which are assumed to vanish at the critical point, implied by the critical slowing down observed in either the realistic experiments or the computer simulation of the phase transition [8][9][10][11][12]. The vanishing response functions lead to the zero Gaussian curvature.…”

Two-Dimensional Infrared Spectroscopy From the Gas to Liquid Phase: Density Dependent J-Scrambling, Vibrational Relaxation, and the Onset of Liquid Character

“…[12][13][14][15][16][17] In addition, the slowing of density fluctuations, due to long range spatial correlations near the critical point, is also a dynamical characteristic of the critical point phase region. [18][19][20][21] Only a relatively few direct time-domain measurements of molecular responses in SCFs have been reported. These include some vibrationally resonant ultrafast pump-probe experiments.…”