Does the Gaussian thermostat maximize the phase-space compression factor?

A recent hypothesis of D. J. Evans and A. Baranyai according to which the Gaussian thermostat maximizes the average phase-space compression factor in nonequilibrium steady states is analyzed for a dilute gas under uniform shear flow. Three routes have been followed: (i) an exact solution of the Bhatnagar-Gross-Krook kinetic equation for arbitrary shear rate, (ii) an exact solution of the Boltzmann equation through super-Burnett order, and (iii) a numerical solution of the Boltzmann equation for finite shear rates. The results show that the above hypothesis does not exactly hold for arbitrary shear rates, although the thermostat that maximizes is close to the Gaussian one. In addition, the influence of the thermostat considered on the nonlinear shear viscosity is also analyzed.     

Positivity of entropy production in the presence of a random thermostat

We study nonequilibrium statistical mechanics in the presence of a thermostat acting by random forces, and propose a formula for the rate of entropy productione() in a state . When is a natural nonequilibrium steady state we show thate()0, and sometimes we can provee()>0.     

A quantum generalization of equilibrium statistical thermodynamics: Effective macroparameters

We propose a generalization of statistical thermodynamics in which quantum effects are taken into account on the macrolevel without explicitly using the operator formalism while traditional relations between the macroparameters are preserved. In a generalized thermostat model, thermal equilibrium is characterized by an effective temperature bounded from below. We introduce fundamental theoretical macroparameters: the effective entropy and the effective action. Because the effective entropy is nonzero at low temperatures, we can write the third law of thermodynamics in the form postulated by Nernst. The effective action at any temperature coincides with the product of standard deviations of the coordinate and momentum in the Heisenberg uncertainty relation and is therefore bounded from below. We establish that the ratio of the effective action to the effective entropy in the low-temperature limit is determined by a holistic stochastic-action constant depending on the Planck and Boltzmann constants. We show that the same results can be obtained in the framework of a modified version of thermofield dynamics in which the quantum oscillator is described by a temperature-dependent complex macroscopic wave function. We study the discrepancy between the behavior of the action-to-entropy ratio in the low-temperature limit in our proposed theory and that in quantum equilibrium statistical mechanics, which can be verified experimentally. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 1, pp. 183–196, January, 2008.     

Influence of temperature, friction, and random forces on folding of the B-domain of staphylococcal protein A: all-atom molecular dynamics in implicit solvent

The influences of temperature, friction, and random forces on the folding of protein A have been analyzed. A series of all-atom molecular dynamics folding simulations with the Amber ff99 potential and Generalized Born solvation, starting from the fully extended chain, were carried out for temperatures from 300 to 500 K, using (a) the Berendsen thermostat (with no explicit friction or random forces) and (b) Langevin dynamics (with friction and stochastic forces explicitly present in the system). The simulation temperature influences the relative time scale of the major events on the folding pathways of protein A. At lower temperatures, helix 2 folds significantly later than helices 1 and 3. However, with increasing temperature, the folding time of helix 2 approaches the folding times of helices 1 and 3. At lower temperatures, the complete formation of secondary and tertiary structure is significantly separated in time whereas, at higher temperatures, they occur simultaneously. These results suggest that some earlier experimental and theoretical observations of folding events, e.g., the order of helix formation, could depend on the temperature used in those studies. Therefore, the differences in temperature used could be one of the reasons for the discrepancies among published experimental and computational studies of the folding of protein A. Friction and random forces do not change the folding pathway that was observed in the simulations with the Berendsen thermostat, but their explicit presence in the system extends the folding time of protein A.     

居中热库蛙跳算法的大尺度模拟测试

分子动力学模拟一个必不可少的要素是对运动方程的准确高效积分. 尽管在动力学传播框架内的现代计算工具中大量使用了传统的蛙跳算法,研究表明蛙跳算法仍然可以进一步改进以获得更好的性能. 居中控温方案中蛙跳的改进版本(蛙跳-middle)实现了更高的精度和效率,即使积分时间步长扩大了几倍,也能保持稳定的动力学传播. 本文使用常规和增强采样模拟中对两个积分算法(蛙跳和蛙跳-middle)进行大尺度模拟测试,旨在标定由时间步长引起的全局性质(例如,详细的势能项)的变化行为以及复杂系统的实际模拟中的局部可观察量(例如,自由能变化或键长). 测试集由六个化学和生物相关系统组成,包括$N$-甲基乙酰胺和A₇-T₇DNA中二面角翻转的构象变化、丙二醛内的分子内质子转移、苯和苯酚针对T4溶菌酶L99A的结合自由能计算、乙胺醇低共熔溶剂中的羟基键长变化以及蓝光受体蛋白的势能计算. 所有结果显示蛙跳-middle积分算法中时间步长引起的误差较小. 蛙跳-middle相对传统蛙跳积分算法的性能提高对于全局属性比局部可观测量更大. 总体而言,目前的工作结果表明,在实际化学和生物系统的模拟中,应优先应用蛙跳-middle算法以获得准确的热力学行为和性质.     

A Gentle Stochastic Thermostat for Molecular Dynamics

We discuss a dynamical technique for sampling the canonical measure in molecular dynamics. We present a method that generalizes a recently proposed scheme (Samoletov et al., J. Stat. Phys. 128:1321–1336, 2007), and which controls temperature by use of a device similar to that of Nosé dynamics, but adds random noise to improve ergodicity. In contrast to Langevin dynamics, where noise is added directly to each physical degree of freedom, the new scheme relies on an indirect coupling to a single Brownian particle. For a model with harmonic potentials, we show under a mild non-resonance assumption that we can recover the canonical distribution. In spite of its stochastic nature, experiments suggest that it introduces a relatively weak perturbative effect on the physical dynamics, as measured by perturbation of temporal autocorrelation functions. The kinetic energy is well controlled even in the early stages of a simulation.     

热超构材料：几何结构、工作机制与新奇性质

因为在热保护、热探测和热管理领域存在重要的应用价值,自由操控宏观热流一直是人类的 一个梦想。热超构材料正是为此目的应运而生,它是电磁超构材料在热学领域的延伸。在此,我将 综述该领域自2008 年诞生以来取得的若干研究进展,其将主要包括以下新奇热现象或功能器件： 热隐身;热聚集;热旋转;宏观热二极管;热伪装;热透明;热晶体;环境温差中零能耗保温;宏 观热网络中反常热传导;热对流隐身、聚集、伪装;热辐射制冷。我将介绍与之相关的微观或宏观 传热机制,这些机制可以通过以下理论或方法来理解或阐述：变换热学理论、Laplace 方程、热声 子能带理论、相变理论、变换热对流理论、热辐射制冷理论。我也将介绍这些材料从基础研究到工 业应用的发展前景。     

理解随机过程分子动力学中的真实/虚拟动力学

Molecular dynamics with the stochastic process provides a convenient way to compute structural and thermodynamic properties of chemical, biological, and materials systems. It is demonstrated that the virtual dynamics case that we proposed for the Langevin equation[J. Chem. Phys. 147, 184104 (2017)] in principle exists in other types of stochastic thermostats as well. The recommended "middle" scheme[J. Chem. Phys. 147, 034109 (2017)] of the Andersen thermostat is investigated as an example. As shown by both analytic and numerical results, while the real and virtual dynamics cases approach the same plateau of the characteristic correlation time in the high collision frequency limit, the accuracy and efficiency of sampling are relatively insensitive to the value of the collision frequency in a broad range. After we compare the behaviors of the Andersen thermostat to those of Langevin dynamics, a heuristic schematic representation is proposed for understanding efficient stochastic thermostatting processes with molecular dynamics.     

Diffusion in a periodic Lorentz gas

We use a constant driving forceF _d together with a Gaussian thermostatting constraint forceF _d to simulate a nonequilibrium steady-state current (particle velocity) in a periodic, two-dimensional, classical Lorentz gas. The ratio of the average particle velocity to the driving force (field strength) is the Lorentz-gas conductivity. A regular Galton-board lattice of fixed particles is arranged in a dense triangular-lattice structure. The moving scatterer particle travels through the lattice at constant kinetic energy, making elastic hard-disk collisions with the fixed particles. At low field strengths the nonequilibrium conductivity is statistically indistinguishable from the equilibrium Green-Kubo estimate of Machta and Zwanzig. The low-field conductivity varies smoothly, but in a complicated way, with field strength. For moderate fields the conductivity generally decreases nearly linearly with field, but is nearly discontinuous at certain values where interesting stable cycles of collisions occur. As the field is increased, the phase-space probability density drops in apparent fractal dimensionality from 3 to 1. We compare the nonlinear conductivity with similar zero-density results from the two-particle Boltzmann equation. We also tabulate the variation of the kinetic pressure as a function of the field strength,