arXiv subjects

Jason R. Green

Publications and source records attributed to Jason R. Green.

23 records · Page 2Linked to original sources

arXiv2018

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.

cond-mat.stat-mech↗

arXiv2018

Nonequilibrium uncertainty principle from information geometry

With a statistical measure of distance, we derive a classical uncertainty relation for processes traversing nonequilibrium states both transiently and irreversibly. The geometric uncertainty associated with dynamical histories that we define is an upper bound for the entropy production and flow rates, but it does not necessarily correlate with the shortest distance to equilibrium. For a model one-bit memory device, we find that expediting the erasure protocol increases the maximum dissipated heat and geometric uncertainty. A driven version of Onsager's three-state model shows that a set of dissipative, high-uncertainty initial conditions, some of which are near equilibrium, scar the state space.

cond-mat.stat-mech↗

arXiv2017

Self-averaging fluctuations in the chaoticity of simple fluids

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.

cond-mat.stat-mech↗

arXiv2015

Order and disorder in irreversible decay processes

Dynamical disorder motivates fluctuating rate coefficients in phenomenological, mass-action rate equations. The reaction order in these rate equations is the fixed exponent controlling the dependence of the rate on the number of species. Here we clarify the relationship between these notions of (dis)order in irreversible decay, $n\,A\to B$, $n=1,2,3,\ldots$, by extending a theoretical measure of fluctuations in the rate coefficient. The measure, $\mathcal{J}_n-\mathcal{L}_n^2\geq 0$, is the magnitude of the inequality between $\mathcal{J}_n$, the time-integrated square of the rate coefficient multiplied by the time interval of interest, and $\mathcal{L}_n^2$, the square of the time-integrated rate coefficient. Applying the inequality to empirical models for non-exponential relaxation, we demonstrate that it quantifies the cumulative deviation in a rate coefficient from a constant, and so the degree of dynamical disorder. The equality is a bound satisfied by traditional kinetics where a single rate constant is sufficient. For these models, we show how increasing the reaction order can increase or decrease dynamical disorder and how, in either case, the inequality $\mathcal{J}_n-\mathcal{L}_n^2\geq 0$ can indicate the ability to deduce the reaction order in dynamically disordered kinetics.

cond-mat.stat-mech↗

arXiv2014

Measuring disorder in irreversible decay processes

Rate coefficients can fluctuate in statically and dynamically disordered kinetics. Here we relate the rate coefficient for an irreversibly decaying population to the Fisher information. From this relationship we define kinetic versions of statistical-length squared and divergence that measure cumulative fluctuations in the rate coefficient. We show the difference between these kinetic quantities measures the amount of disorder, and is zero when the rate coefficient is temporally and spatially unique.

cond-mat.stat-mech↗