A Framework for Non-Equilibrium Statistical Ensemble Theory

Since Gibbs synthesized a general equilibrium statistical ensemble theory, many theorists have attempted to generalized the Gibbsian theory to
non-equilibrium phenomena domain, however the status of the theory of non-equilibrium phenomena can not be said as firm as well established as the
Gibbsian ensemble theory. In this work, we present a framework for the non-equilibrium statistical ensemble formalism based on a subdynamic kinetic
equation (SKE) rooted from the Brussels-Austin school and followed by some up-to-date works. The constructed key is to use a similarity transformation between Gibbsian ensembles formalism based on Liouville equation and the subdynamic ensemble formalism based on the SKE. Using this formalism, we study the spin-Boson system, as cases of weak coupling or strongly coupling, and obtain the reduced density operators for the Canonical ensembles easily.     

Statistical physics of shear flow: a non-equilibrium problem

Complex fluids are easily and reproducibly driven into non-equilibrium steady states by the action of shear flow. The statistics of the microstructure of non-equilibrium fluids is important to the material properties of every complex fluid that flows, e.g. axle grease on a rotating bearing; blood circulating in capillaries; molten plastic flowing into a mould; the non-equilibrium onion phase of amphiphiles used for drug delivery; the list is endless. Such states are as diverse and interesting as equilibrium states, but are not governed by the same statistics as equilibrium materials. I review some recently discovered principles governing the probabilities of various types of molecular re-arrangements taking place within a sheared fluid. As well as providing new foundations for the study of non-equilibrium matter, the principles are applied to some simple models of particles interacting under flow, showing that the theory exhibits physically convincing behaviour.     

Mathematical Theory of Non-Equilibrium Quantum Statistical Mechanics

We review and further develop a mathematical framework for non-equilibrium quantum statistical mechanics recently proposed in refs. 1–7. In the algebraic formalism of quantum statistical mechanics we introduce notions of non-equilibrium steady states, entropy production and heat fluxes, and study their properties. Our basic paradigm is a model of a small (finite) quantum system coupled to several independent thermal reservoirs. We exhibit examples of such systems which have strictly positive entropy production.     

Macroscopic Fluctuation Theory for Stationary Non-Equilibrium States

We formulate a dynamical fluctuation theory for stationary non-equilibrium states (SNS) which is tested explicitly in stochastic models of interacting particles. In our theory a crucial role is played by the time reversed dynamics. Within this theory we derive the following results: the modification of the Onsager–Machlup theory in the SNS; a general Hamilton–Jacobi equation for the macroscopic entropy; a non-equilibrium, nonlinear fluctuation dissipation relation valid for a wide class of systems; an H theorem for the entropy. We discuss in detail two models of stochastic boundary driven lattice gases: the zero range and the simple exclusion processes. In the first model the invariant measure is explicitly known and we verify the predictions of the general theory. For the one dimensional simple exclusion process, as recently shown by Derrida, Lebowitz, and Speer, it is possible to express the macroscopic entropy in terms of the solution of a nonlinear ordinary differential equation; by using the Hamilton–Jacobi equation, we obtain a logically independent derivation of this result.     

湿蒸汽非平衡态凝结流动的数值方法研究

在欧拉-欧拉、非结构有限体积框架下发展了湿蒸汽非平衡态凝结流动的数值方法。推导了基于真实物性,密度、内能和湿度全耦合的Roe通量。提出了适用于欧拉-欧拉法的三自由度TTSE水蒸气表。使用矩方法(MOM)和积分矩方法(QMOM)模拟水珠半径分布,并就时间推进时QMOM方法的不稳定现象给出了修正方法。通过两个无黏喷管和一个湍流平面叶栅算例进行了验证,表明本文的数值方法能比较准确地捕捉非平衡态凝结现象。     

Quantum Retrodiction in Non-Equilibrium Thermo Field Dynamics

The quantum retrodiction for open systems which obey the quantum Markovian dynamics is investigated by means of non-equilibrium thermo Field dynamics (NETFD) which can easily derive the retrodictive time-evolution generators. NETFD can formulate the quantum retrodiction for open systems in the same way as that for closed systems.     

非平衡态辐射场能量状态参数的表征

本文提出了非平衡态辐射体系的热力学框架,以光子的能量、光子的有效能、光子的熵、光子的特征温度为基础,把辐射热力学体系分解为边界和辐射场进行描述,给出了非平衡态辐射场中辐射能状态参数的表征式,提出了表征任意指定照射窗口的照射辐射特征温度概念,结合照射辐射强度、照射辐射能量等效温度,表征了辐射场的能量强度、有效能和熵等热力学参数。     

Response Theory for Equilibrium and Non-Equilibrium Statistical Mechanics: Causality and Generalized Kramers-Kronig Relations

We consider the general response theory recently proposed by Ruelle for describing the impact of small perturbations to the non-equilibrium steady states resulting from Axiom A dynamical systems. We show that the causality of the response functions entails the possibility of writing a set of Kramers-Kronig (K-K) relations for the corresponding susceptibilities at all orders of nonlinearity. Nonetheless, only a special class of directly observable susceptibilities obey K-K relations. Specific results are provided for the case of arbitrary order harmonic response, which allows for a very comprehensive K-K analysis and the establishment of sum rules connecting the asymptotic behavior of the harmonic generation susceptibility to the short-time response of the perturbed system. These results set in a more general theoretical framework previous findings obtained for optical systems and simple mechanical models, and shed light on the very general impact of considering the principle of causality for testing self-consistency: the described dispersion relations constitute unavoidable benchmarks that any experimental and model generated dataset must obey. The theory exposed in the present paper is dual to the time-dependent theory of perturbations to equilibrium states and to non-equilibrium steady states, and has in principle similar range of applicability and limitations. In order to connect the equilibrium and the non equilibrium steady state case, we show how to rewrite the classical response theory by Kubo so that response functions formally identical to those proposed by Ruelle, apart from the measure involved in the phase space integration, are obtained. These results, taking into account the chaotic hypothesis by Gallavotti and Cohen, might be relevant in several fields, including climate research. In particular, whereas the fluctuation-dissipation theorem does not work for non-equilibrium systems, because of the non-equivalence between internal and external fluctuations, K-K relations might be robust tools for the definition of a self-consistent theory of climate change.     

A Fast and Efficient Ensemble Transfer Entropy and Applications in Neural Signals

The ensemble transfer entropy (TEensemble) refers to the transfer entropy estimated from an ensemble of realizations. Due to its time-resolved analysis, it is adapted to analyze the dynamic interaction between brain regions. However, in the traditional TEensemble, multiple sets of surrogate data should be used to construct the null hypothesis distribution, which dramatically increases the computational complexity. To reduce the computational cost, a fast, efficient TEensemble with a simple statistical test method is proposed here, in which just one set of surrogate data is involved. To validate the improved efficiency, the simulated neural signals are used to compare the characteristics of the novel TEensemble with those of the traditional TEensemble. The results show that the time consumption is reduced by two or three magnitudes in the novel TEensemble. Importantly, the proposed TEensemble could accurately track the dynamic interaction process and detect the strength and the direction of interaction robustly even in the presence of moderate noises. The novel TEensemble reaches its steady state with the increased samples, which is slower than the traditional method. Furthermore, the effectiveness of the novel TEensemble was verified in the actual neural signals. Accordingly, the TEensemble proposed in this work may provide a suitable way to investigate the dynamic interactions between brain regions.     

涌现于交叉科学的新方向——活性物质

活性物质是一类由自驱动个体组成的非平衡系统,存在于从宏观到微观的各个尺度,典型例子包括动物群落、细胞组织、微纳米机器、分子马达等。活性物质的组成个体可以通过消耗局域存储的自由能打破细致平衡、实现自驱动运动,同时通过相互作用形成众多的集体行为,比如自发流动、无序—有序相变、运动的拓扑缺陷等。文章聚焦活性物质的集体行为,从理论和实验的角度揭示这些行为的形成机制和非平衡特征,并讨论活性物质研究在生物、数学和工程等学科中的影响和可能应用。     

Non-Equilibrium Entropy and Irreversibility in Generalized Stochastic Loewner Evolution from an Information-Theoretic Perspective

In this study, we theoretically investigated a generalized stochastic Loewner evolution (SLE) driven by reversible Langevin dynamics in the context of non-equilibrium statistical mechanics. Using the ability of Loewner evolution, which enables encoding of non-equilibrium systems into equilibrium systems, we formulated the encoding mechanism of the SLE by Gibbs entropy-based information-theoretic approaches to discuss its advantages as a means to better describe non-equilibrium systems. After deriving entropy production and flux for the 2D trajectories of the generalized SLE curves, we reformulated the system’s entropic properties in terms of the Kullback–Leibler (KL) divergence. We demonstrate that this operation leads to alternative expressions of the Jarzynski equality and the second law of thermodynamics, which are consistent with the previously suggested theory of information thermodynamics. The irreversibility of the 2D trajectories is similarly discussed by decomposing the entropy into additive and non-additive parts. We numerically verified the non-equilibrium property of our model by simulating the long-time behavior of the entropic measure suggested by our formulation, referred to as the relative Loewner entropy.     

Covariant Non-Equilibrium Transport Theory Solutions for RHIC

New numerical solutions of 3+1D covariant kinetic theory are reported for nuclear collisions in the energy domain E_cm200 AGeV. They were obtained using the MPC 0.1.2 parton transport code employing high parton subdivision to retain Lorentz covariance. The solutions are compared to those of relativistic hydrodynamics employing Cooper–Frye isotherm freeze-out. The transport solutions follow a different dynamical path than hydrodynamics due to large dissipative effects when pQCD scattering rates and HIJING initial conditions are assumed. The transport freeze-out four-volume is sensitive to the reaction rates. The final transverse momentum distributions are found to deviate by up to an order of magnitude from those of Cooper–Frye frozen hydrodynamics.     

Statistical Gauge Theory for Relativistic Finite Density Problems

A relativistic quantum field theory is presented for finite density problems based on the principle of locality.It is shown that,in addition to the conventional ones,a local approach to the relativistic quantum field theories at both zero and finite densities consistent with the violation of Bell-like inequalities should contain and provide solutions to at least three additional problems,namely,i) the statistical gauge invariance;ii) the dark components of the local observables;and iii)the fermion statistical blocking effects,based upon an asymptotic nonthermal ensemble,An application to models is presented to show the importance of the discussions.     

系综Monte Carlo方法

本文系统地给出了Monte Carlo模拟的一般方法在各种系综条件下的表述以及它们的算法。     

A Pragmatic Ensemble Strategy for Missing Values Imputation in Health Records

Pristine and trustworthy data are required for efficient computer modelling for medical decision-making, yet data in medical care is frequently missing. As a result, missing values may occur not just in training data but also in testing data that might contain a single undiagnosed episode or a participant. This study evaluates different imputation and regression procedures identified based on regressor performance and computational expense to fix the issues of missing values in both training and testing datasets. In the context of healthcare, several procedures are introduced for dealing with missing values. However, there is still a discussion concerning which imputation strategies are better in specific cases. This research proposes an ensemble imputation model that is educated to use a combination of simple mean imputation, k-nearest neighbour imputation, and iterative imputation methods, and then leverages them in a manner where the ideal imputation strategy is opted among them based on attribute correlations on missing value features. We introduce a unique Ensemble Strategy for Missing Value to analyse healthcare data with considerable missing values to identify unbiased and accurate prediction statistical modelling. The performance metrics have been generated using the eXtreme gradient boosting regressor, random forest regressor, and support vector regressor. The current study uses real-world healthcare data to conduct experiments and simulations of data with varying feature-wise missing frequencies indicating that the proposed technique surpasses standard missing value imputation approaches as well as the approach of dropping records holding missing values in terms of accuracy.     

Derivation of Mayer Series from Canonical Ensemble

Mayer derived the Mayer series from both the canonical ensemble and the grand canonical ensemble by use of the cluster expansion method. In 2002, we conjectured a recursion formula of the canonical partition function of a fluid(X.Z. Wang, Phys. Rev. E66(2002) 056102). In this paper we give a proof for this formula by developing an appropriate expansion of the integrand of the canonical partition function. We further derive the Mayer series solely from the canonical ensemble by use of this recursion formula.     

A new approach for the justification of ensembles in quantum statistical mechanics — I

In this and the following paper, a new approach for the justification of ensembles in statistical mechanics is given. The essential physical idea is that a measurement is an average of values arising from disjoint regions in three-space. This idea is given a mathematical basis in terms of a class of operators called local operators, and the first paper is devoted primarily to the development of the properties of local operators. In particular, a complete characterization of the bounded local operators on ₂ spaces of finite measure is given. Two results of importance for statistical mechanics are also derived. First, it is shown that the observables of quantum mechanics are local operators. Second, it is shown that the expectation value of an observable for a pure state can be written formally as an ensemble average. In the following paper, these results are used to develop a new approach for the justification of statistical ensembles.This work was supported in part by research grants from the National Science Foundation and the U.S. Public Health Service. The material of this paper is contained in a doctoral dissertation submitted by the author to the University of Oregon (1969).     

一种获取三肽构象系综的可靠量子化学方法

三肽是蛋白质的基本组成模块, 具有重要生理功能. 解析其结构对于更大的肽及蛋白质研究具有重要意义. 基于二面角组合规则, 结合键旋转手段, 提出一种获取三肽构象系综的从头算量子化学方法. 使用该方法对八个目标三肽的势能面进行彻底搜索, 将所得结果与以前的预测方法及蛋白质数据库(PDB) 提取的结构进行比较.结果表明, 新方法搜索到了最完整的三肽构象系综. 此外证明了 PDB 结构存在缺陷, 遗漏了大部分中低能区的重要构象. 将新获取的三肽结构用于红外光谱研究, 理论结果与实验数据符合得更精准.