A NEW APPROACH TO NONEQUILIBRIUM STATISTICAL MECHANICS OF GASES
Gas dynamics - nonequilibrium statistical mechanics
RAREFIED GAS DYNAMICS↗
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Random paths and current fluctuations in nonequilibrium statistical mechanics
An overview is given of recent advances in nonequilibrium statistical mechanics about the statistics of random paths and current fluctuations. Although statistics is carried out in space for equilibrium statistical mechanics, statistics is considered in time or spacetime for nonequilibrium systems. In this approach, relationships have been established between nonequilibrium properties such as the transport coefficients, the thermodynamic entropy production, or the affinities, and quantities characterizing the microscopic Hamiltonian dynamics and the chaos or fluctuations it may generate. This overview presents results for classical systems in the escape-rate formalism, stochastic processes, and open quantum systems.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DRACO and Nonequilibrium Statistical Mechanics of Aging [Slides]
Topics covered include: Types of problems which DRACO (Multiphysics simulation) was designed to address; Tools from nonequilibrium statistical mechanics; Rare events (Extreme value statistics); Transients (Diverging time scales); and, Thresholds (Absorbing phase transitions).
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Nonequilibrium statistical mechanics and optimal prediction of partially-observed complex systems
Abstract Only a subset of degrees of freedom are typically accessible or measurable in real-world systems. As a consequence, the proper setting for empirical modeling is that of partially-observed systems. Notably, data-driven models consistently outperform physics-based models for systems with few observable degrees of freedom; e.g. hydrological systems. Here, we provide an operator-theoretic explanation for this empirical success. To predict a partially-observed system’s future behavior with physics-based models, the missing degrees of freedom must be explicitly accounted for using data assimilation and model parametrization. Data-driven models, in contrast, employ delay-coordinate embeddings and their evolution under the Koopman operator to implicitly model the effects of the missing degrees of freedom. We describe in detail the statistical physics of partial observations underlying data-driven models using novel maximum entropy and maximum caliber measures. The resulting nonequilibrium Wiener projections applied to the Mori–Zwanzig formalism reveal how data-driven models may converge to the true dynamics of the observable degrees of freedom. Additionally, this framework shows how data-driven models infer the effects of unobserved degrees of freedom implicitly, in much the same way that physics models infer the effects explicitly. This provides a unified implicit-explicit modeling framework for predicting partially-observed systems, with hybrid physics-informed machine learning methods combining both implicit and explicit aspects.
97 MATHEMATICS AND COMPUTING↗
Reshaping, Intermixing, and Coarsening for Metallic Nanocrystals: Nonequilibrium Statistical Mechanical and Coarse-Grained Modeling
Self-assembly of supported 2D or 3D nanocrystals (NCs) by vacuum deposition and of 3D NCs by solution-phase synthesis (with possible subsequent transfer to a support) produces intrinsically nonequilibrium systems. Individual NCs can have far-from-equilibrium shapes and composition profiles. The free energy of NC ensembles is lowered by coarsening which can involve Ostwald ripening or Smoluchowski ripening (NC diffusion and coalescence). Preservation of individual NC structure and inhibition of coarsening are key, e.g., for avoiding catalyst degradation. This review focuses on postsynthesis evolution of metallic NCs. Atomistic-level modeling typically utilizes stochastic lattice-gas models to access appropriate time and length scales. However, predictive modeling requires incorporation of realistic rates for relaxation mechanisms, e.g., periphery diffusion and intermixing, in numerous local environments (rather than the use of generic prescriptions). Alternative coarse-grained modeling must also incorporate appropriate mechanisms and kinetics. At the level of individual NCs, we present analyses of reshaping, including sintering and pinch-off, and of compositional evolution in a vacuum environment. Here, we also discuss modeling of coarsening including diffusion and decay of individual NCs and unconventional coarsening processes. We describe high-level modeling integrated with scanning tunneling microscopy (STM) studies for supported 2D epitaxial nanoclusters and developments in modeling for 3D NCs motivated by in situ transmission electron microscopy (TEM) studies.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Nonequilibrium Statistical Mechanics: potential applications in biology
The purpose of this project is to create fast, accurate simulations of complex large-scale systems with a quantified, predicitive capability.
59 BASIC BIOLOGICAL SCIENCES↗
Unifying Quantum and Classical Speed Limits on Observables
Not Available
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
The application of statistical mechanics of nonequilibrium processes to astrophysics and the determination of galactic mass distribution and gravitational potential Final report
Application of statistical mechanics of nonequilibrium processes to astrophysics and determination of galactic mass distribution and gravitational potential
NONEQUILIBRIUM↗
Fredkin Staircase: An Integrable System with a Finite-Frequency Drude Peak
We introduce and explore an interacting integrable cellular automaton, the Fredkin staircase, that lies outside the existing classification of such automata, and has a structure that seems to lie beyond that of any existing Bethe-solvable model. The Fredkin staircase has two families of ballistically propagating quasiparticles, each with infinitely many species. Despite the presence of ballistic quasiparticles, charge transport is diffusive in the d.c. limit, albeit with a highly non- gaussian dynamic structure factor. Remarkably, this model exhibits persistent temporal oscillations of the current, leading to a delta-function singularity (Drude peak) in the a.c. conductivity at nonzero frequency. Here, we analytically construct an extensive set of operators that anticommute with the time-evolution operator; the existence of these operators both demonstrates the integrability of the model and allows us to lower-bound the weight of this finite-frequency singularity.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Strongly magnetized classical plasma models
Discrete particle processes in the presence of a strong external magnetic field were investigated. These processes include equations of state and other equilibrium thermodynamic relations, thermal relaxation phenomena, transport properties, and microscopic statistical fluctuations in such quantities as the electric field and the charge density. Results from the equilibrium statistical mechanics of two-dimensional plasmas are discussed, along with nonequilibrium statistical mechanics of the electrostatic guiding-center plasma (a two-dimensional plasma model).
Montgomery, D.↗
Entropy production in model colloidal suspensions under shear via the fluctuation theorem
Dissipative systems often exhibit novel and unexpected properties. This is, for instance, the case of simple liquids, which, when subjected to shear and after reaching a steady state, can exhibit a negative entropy production over finite length scales and timescales. This result, among others, is captured by nonequilibrium relations known as fluctuation theorems. Using nonequilibrium molecular dynamics simulations, we examine how, by fine-tuning the properties of the components of a complex fluid, we can steer the nonequilibrium response of the fluid. More specifically, we show how we control the nonequilibrium probability distribution for the shear stress and, in turn, how often states with a negative entropy production can occur. To achieve this, we start by characterizing how the size for the liquid matrix impacts the probability of observing negative entropy states, as well as the timescale over which these can be observed. We then measure how the addition of larger particles to this liquid matrix, i.e., simulating a model colloidal suspension, results in an increase in the occurrence of such states. As a result, this suggests how modifications in the composition of the mixture and in the properties of its components lead to an increase in the probability of observing states of negative entropy production and, thus, for the system to run in reverse.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Lectures on statistical mechanics
Presented here is a transcription of the lecture notes from Professor Allan N. Kaufman’s graduate statistical mechanics course Physics 212A and 212B at the University of California Berkeley from the 1972–1973 academic year. 212A addressed equilibrium statistical mechanics with topics: fundamentals (micro-canonical and sub-canonical ensembles, adiabatic law and action conservation, fluctuations, pressure, and virial theorem), classical fluids and other systems (equation of state, deviations from ideality, virial coefficients and van der Waals potential, canonical ensemble and partition function, quasistatic evolution, grand-canonical ensemble and partition function, chemical potential, simple model of a phase transition, quantum virial expansion, numerical simulation of equations of state, and phase transition), chemical equilibrium (systems with multiple species and chemical reactions, law of mass action, Saha equation, chemical equilibrium including ionization and excited states), and long-range interactions (including Coulomb, dipole, and gravitational interactions, Debye–Hückel theory, and shielding). 212B addressed nonequilibrium statistical mechanics with topics: fundamentals (definitions: realizations, moments, characteristic function, and discrete variables), Brownian motion (Langevin equation, fluctuation–dissipation theorem, spatial diffusion, Boltzmann’s H-theorem), Liouville and Klimontovich equations, Landau equation (derivation, elaboration, and H-theorem, and irreversibility), Markov processes and Fokker–Planck equation (derivations of the Fokker–Planck equation and a master equation), linear response and transport theory (linear Boltzmann equation, linear response theory of Kubo and Mori, relation of entropy production to electrical conductivity, transport relations and coefficients, normal mode solutions of the transport equations, sketch of a generalized Langevin equation method for transport theory), and an introduction to nonequilibrium quantum statistical mechanics.
plasma dynamics↗
Tests for, origins of, and corrections to non-Gaussian statistics. The dipole-flip model
Linear response approximations are central to our understanding and simulations of nonequilibrium statistical mechanics. Despite the success of these approaches in predicting nonequilibrium dynamics, open questions remain. Laird and Thompson [J. Chem. Phys. 126, 211104 (2007)] previously formalized, in the context of solvation dynamics, the connection between the static linear-response approximation and the assumption of Gaussian statistics. The Gaussian statistics perspective is useful in understanding why linear response approximations are still accurate for perturbations much larger than thermal energies. In this study, we use this approach to address three outstanding issues in the context of the “dipole-flip” model, which is known to exhibit nonlinear response. First, we demonstrate how non-Gaussian statistics can be predicted from purely equilibrium molecular dynamics (MD) simulations (i.e., without resort to a full nonequilibrium MD as is the current practice). Second, we show that the Gaussian statistics approximation may also be used to identify the physical origins of nonlinear response residing in a small number of coordinates. Third, we explore an approach for correcting the Gaussian statistics approximation for nonlinear response effects using the same equilibrium simulation. Finally, the results are discussed in the context of several other examples of nonlinear responses throughout the literature.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Mean-field control for efficient mixing of energy loads
In this work, we pose an engineering challenge of controlling an ensemble of energy devices via coordinated, implementation-light, and randomized on/off switching as a problem in nonequilibrium statistical mechanics. We show that mean-field control with nonlinear feedback on the cumulative consumption, assumed available to the aggregator via direct physical measurements of the energy flow, allows the ensemble to recover from its use in the demand response regime, i.e., transition to a statistical steady state, significantly faster than in the case of the fixed feedback. Moreover when the nonlinearity is sufficiently strong, one observes the phenomenon of “super-relaxation,” where the total instantaneous energy consumption of the ensemble transitions to the steady state much faster than the underlying probability distribution of the devices over their state space, while also leaving almost no devices outside of the comfort zone.
25 ENERGY STORAGE↗
Probabilistic measures for biological adaptation and resilience
This paper introduces an approach to quantifying ecological resilience in biological systems, particularly focusing on noisy systems responding to episodic disturbances with sudden adaptations. Incorporating concepts from nonequilibrium statistical mechanics, we propose a measure termed “ecological resilience through adaptation,” specifically tailored to noisy, forced systems that undergo physiological adaptation in the face of stressful environmental changes. Randomness plays a key role, accounting for model uncertainty and the inherent variability in the dynamical response among components of biological systems. Our measure of resilience is rooted in the probabilistic description of states within these systems and is defined in terms of the dynamics of the ensemble average of a model-specific observable quantifying success or well-being. Our approach utilizes stochastic linear response theory to compute how the expected success of a system, originally in statistical equilibrium, dynamically changes in response to a environmental perturbation and a subsequent adaptation. Importantly, the resulting mathematical derivations allow for the estimation of resilience in terms of ensemble averages of simulated or experimental data. Finally, through a simple but clear conceptual example, we illustrate how our resilience measure can be interpreted and compared to other existing frameworks in the literature. The methodology is general but inspired by applications in plant systems, with the potential for broader application to complex biological processes.
60 APPLIED LIFE SCIENCES↗
Statistical mechanics of neocortical interactions - Dynamics of synaptic modification
A recent study has demonstrated that several scales of neocortical interactions can be consistently analyzed with the use of methods of modern nonlinear nonequilibrium statistical mechanics. The formation, stability, and interaction of spatial-temporal patterns of columnar firings are explicitly calculated, to test hypothesized mechanisms relating to information processing. In this context, most probable patterns of columnar firings are associated with chemical and electrical synaptic modifications. It is stressed that synaptic modifications and shifts in most-probable firing patterns are highly nonlinear and interactive sets of phenomena. A detailed scenario of information processing is calculated of columnar coding of external stimuli, short-term storage via hysteresis, and long-term storage via synaptic modification.
Ingber, L.↗
Strongly magnetized classical plasma models
The class of plasma processes for which the so-called Vlasov approximation is inadequate is investigated. Results from the equilibrium statistical mechanics of two-dimensional plasmas are derived. These results are independent of the presence of an external dc magnetic field. The nonequilibrium statistical mechanics of the electrostatic guiding-center plasma, a two-dimensional plasma model, is discussed. This model is then generalized to three dimensions. The guiding-center model is relaxed to include finite Larmor radius effects for a two-dimensional plasma.
Montgomery, D. C.↗
A comparative study of coarse-graining methods for polymeric fluids: Mori-Zwanzig vs. iterative Boltzmann inversion vs. stochastic parametric optimization
We construct effective coarse-grained (CG) models for polymeric fluids by employing two coarse-graining strategies. The first one is a forward-coarse-graining procedure by the Mori-Zwanzig (MZ) projection while the other one applies a reverse-coarse-graining procedure, such as the iterative Boltzmann inversion (IBI) and the stochastic parametric optimization (SPO). More specifically, we perform molecular dynamics (MD) simulations of star polymer melts to provide the atomistic fields to be coarse-grained. Each molecule of a star polymer with internal degrees of freedom is coarsened into a single CG particle and the effective interactions between CG particles can be either evaluated directly from microscopic dynamics based on the MZ formalism, or obtained by the reverse methods, i.e., IBI and SPO. The forward procedure has no free parameters to tune and recovers the MD system faithfully. For the reverse procedure, we find that the parameters in CG models cannot be selected arbitrarily. If the free parameters are properly defined, the reverse CG procedure also yields an accurate effective potential. Moreover, we explain how an aggressive coarse-graining procedure introduces the many-body effect, which makes the pairwise potential invalid for the same system at densities away from the training point. From this work, general guidelines for coarse-graining of polymeric fluids can be drawn.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗