集合预报物理基础的探讨

将集合预报中的每次积分算程视为非平衡统计物理理论中的准粒子轨迹，由此对Lorenz模型 进行了数值试验，计算了初值位于不同性质平衡态附近时准粒子数处于基态和第一激发态随 时间的演化.结果证明：(1)若动力系统在整个相空间内存在稳定的平衡态，在稳定的平衡态 附近，系统随时间长期演化行为是可预测的.(2)若动力系统在整个相空间内不存在任何稳定 的平衡态，初值位于远离非稳定的平衡态，则在1—2周内准粒子多数分布在低能量态，即预 报是最可几率的.(3)若初始状态位于非稳定平衡态附近，系统随时间的演化几乎是不可预测 的.这从理论上说明了作大量积分算程的集合预报其效果会比单一初值的单程积分要好.这就 从物理上对集合预报能提高准确率提供了一种解释. 关键词： 集合预报 Lorenz模型 正则分布 概率密度分布     

Optical properties of nonequilibrium low-dimensional systems

The optical properties of low-dimensional carrier systems ("quantum wire" type) driven away from equilibrium are studied. The frequency and wave-vector-dependent dielectric function of a quasi-one-dimensional electron system under the action of an exciting external pumping source is derived. The optical responses of the system are obtained in terms of its nonequilibrium thermodynamic state, the latter characterized resorting to a nonequilibrium statistical ensemble formalism.     

Microscopic Analysis of Clausius–Duhem Processes

Given a thermodynamic process which carries a system from one equilibrium state to another, we construct a quantity whose average, over an ensemble of microscopic realizations of the process, depends only on these end states, even if at intermediate times the system is out of equilibrium. This result (1) can be used to express the entropy difference between two equilibrium states in terms of an irreversible process connecting them, (2) leads to two statistical statements of the Clausius–Duhem inequality, and (3) can be generalized to situations in which the system begins and/or ends in nonequilibrium states.     

Observation of a 1/t decay law for hot clusters and molecules in a storage ring

The exponential law is valid both for decay from a single quantum state into a continuum and for an ensemble maintained in thermal equilibrium. For statistical decay of an ensemble of isolated systems with a broad energy distribution, the exponential decay is replaced by a 1/t distribution. We present confirmation of this decay law by experiments with cluster anions in a small electrostatic storage ring. Deviations from the 1/t law for such an ensemble give important information on the dynamics of the systems. As examples, we present measurements revealing strong radiative cooling of anions of both metal clusters and fullerenes.     

Gibbs–Jaynes Entropy Versus Relative Entropy

The maximum entropy formalism developed by Jaynes determines the relevant ensemble in nonequilibrium statistical mechanics by maximising the entropy functional subject to the constraints imposed by the available information. We present an alternative derivation of the relevant ensemble based on the Kullback–Leibler divergence from equilibrium. If the equilibrium ensemble is already known, then calculation of the relevant ensemble is considerably simplified. The constraints must be chosen with care in order to avoid contradictions between the two alternative derivations. The relative entropy functional measures how much a distribution departs from equilibrium. Therefore, it provides a distinct approach to the calculation of statistical ensembles that might be applicable to situations in which the formalism presented by Jaynes performs poorly (such as non-ergodic dynamical systems).     

Thermodynamic aspects of Schrödinger's probability relations

Using Schrödinger's generalized probability relations of quantum mechanics, it is possible to generate a canonical ensemble, the ensemble normally associated with thermodynamic equilibrium, by at least two methods, statistical mixing and subensemble selection, that do not involve thermodynamic equilibration. Thus the question arises as to whether an observer making measurements upon systems from a canonical ensemble can determine whether the systems were prepared by mixing, equilibration, or selection. Investigation of this issue exposes antinomies in quantum statistical thermodynamics. It is conjectured that resolution of these paradoxes may involve a new law of motion in quantum dynamics.     

Substantiating the Gibbs method in classical statistical mechanics

An approach for the substantiation of the Gibbs method in equilibrium statistical thermodynamics is described; this approach is based not on the quasiergodicity hypothesis, but on the weaker assumption of macroscopic determinacy of thermodynamic systems. A generalized microcanonical Gibbs distribution is obtained. An electron gas in a homogeneous magnetic field is taken as an example. It is shown that the classical diamagnetism of the given system is not zero in the sense of quasimean nor of generalized Gibbs ensemble distributions. The equation of state of an electron as in a magnetic field is obtained, and hence it is shown that classical diamagnetism only vanishes if isotropy of the pressure at the vessel wall is assumed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 65–68, June, 1978.     

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.     

Form of growing strings

Patterns and forms adopted by nature are often the results of simple dynamical paradigms. Here we show that a growing self-interacting string attached to a tracking origin, modeled to resemble nascent polypeptides in vivo, develops helical structures which are more pronounced at the growing end. We also show that the dynamic growth ensemble shares several features of an equilibrium ensemble in which the growing end of the polymer is under an effective stretching force. A statistical analysis of native states of proteins shows that the signature of this nonequilibrium phenomenon has been fixed by evolution at the C terminus, the growing end of a nascent protein. These findings suggest how evolution may have built on the properties of a generic nonequilibrium growth process in favoring helical structures in nascent chains.     

Surface pressure in clusters and small particles—is it real?

Using the methods of statistical mechanics and applying the conditions of thermal equilibrium for an ensemble of interacting molecules, it is proved that there is no excess pressure, nor internal and surface stresses, in clusters and small particles that are not subjected to the action of external forces. With this premise taken into account the thermodynamics of spherical and faceted small particles is developed. In a particle-vapour system surrounded by a rigid impervious shell, Kelvin's and Thomson's formulae and Wulff's rule are derived. For a particle-melt system at a constant external pressure it is expected that the melting points of a particle and a bulk solid should be equal. It is noted that, if a particle is not subjected to the action of external fields or bodies, its molecules occupy their natural equilibrium positions, and it is from them that deformations and internal stresses should be counted off. These equilibrium positions differ from those occupied by the same molecules in a bulk solid, which is what usually gives rise to the illusions of the stressed state of a small particle and its deformation caused by the “uncompensated” surface forces.     

Entropy and temperature of a static granular assembly: an ab initio approach

We construct a statistical framework for static assemblies of deformable grains which parallels that of equilibrium statistical mechanics but with a conservation principle based on the mechanical stress tensor. We define a state function that has all the attributes of entropy. In particular, maximizing this function leads to a well-defined granular temperature and the equivalent of the Boltzman distribution for ensembles of grain packings. Predictions of the ensemble are verified against simulated packings of frictionless, deformable disks.     

Thermostating by Deterministic Scattering: The Periodic Lorentz Gas

We present a novel mechanism for thermalizing a system of particles in equilibrium and nonequilibrium situations, based on specifically modeling energy transfer at the boundaries via a microscopic collision process. We apply our method to the periodic Lorentz gas, where a point particle moves diffusively through an ensemble of hard disks arranged on a triangular lattice. First, collision rules are defined for this system in thermal equilibrium. They determine the velocity of the moving particle such that the system is deterministic, time-reversible, and microcanonical. These collision rules can systematically be adapted to the case where one associates arbitrarily many degrees of freedom to the disk, which here acts as a boundary. Subsequently, the system is investigated in nonequilibrium situations by applying an external field. We show that in the limit where the disk is endowed by infinitely many degrees of freedom it acts as a thermal reservoir yielding a well-defined nonequilibrium steady state. The characteristic properties of this state, as obtained from computer simulations, are finally compared to those of the so-called Gaussian thermostated driven Lorentz gas.     

Equilibrium statistical mechanics for incomplete nonextensive statistics

The incomplete nonextensive statistics in the canonical and microcanonical ensembles is explored in the general case and in a particular case for the ideal gas. By exact analytical results for the ideal gas it is shown that taking the thermodynamic limit, with z=q/(1−q) being an extensive variable of state, the incomplete nonextensive statistics satisfies the requirements of equilibrium thermodynamics. The thermodynamical potential of the statistical ensemble is a homogeneous function of the first degree of the extensive variables of state. In this case, the incomplete nonextensive statistics is equivalent to the usual Tsallis statistics. If z is an intensive variable of state, i.e. the entropic index q is a universal constant, the requirements of the equilibrium thermodynamics are violated.     

Jamming I: A volume function for jammed matter

We introduce a “Hamiltonian”-like function, called the volume function, indispensable to describe the ensemble of jammed matter such as granular materials and emulsions from a geometrical point of view. The volume function represents the available volume of each particle in the jammed systems. At the microscopic level, we show that the volume function is the Voronoi volume associated to each particle and in turn we provide an analytical formula for the Voronoi volume in terms of the contact network, valid for any dimension. We then develop a statistical theory for the probability distribution of the volumes in 3d to calculate an average volume function coarse-grained at a mesoscopic level. The salient result is the discovery of a mesoscopic volume function inversely proportional to the coordination number. Our analysis is the first step toward the calculation of macroscopic observables and equations of state using the statistical mechanics of jammed matter, when supplemented by the condition of mechanical equilibrium of jamming that properly defines jammed matter at the ensemble level.     

A new parallel algorithm for simulation of spin glasses on scales of space-time periods of external fields with consideration of relaxation effects

We have investigated the statistical properties of an ensemble of disordered 1D spatial spin chains (SSCs) of finite length, placed in an external field, with consideration of relaxation effects. The short-range interaction complex-classical Hamiltonian was first used for solving this problem. A system of recurrent equations is obtained on the nodes of the spin-chain lattice. An efficient mathematical algorithm is developed on the basis of these equations with consideration of advanced Sylvester conditions which allows one to step by step construct a huge number of stable spin chains in parallel. The distribution functions of different parameters of spin glass system are constructed from first principles by analyzing the calculation results of the 1D SSCs ensemble. It is shown that the behaviors of different distributions parameters are quite different even at weak external fields. The ensemble energy and constants of spin-spin interactions are being changed smoothly depending on the external field in the limit of statistical equilibrium, while some of them such as the mean value of polarizations of the ensemble and parameters of its orderings are frustrated. We have also studied some critical properties of the ensemble such as catastrophes in the Clausius-Mossotti equation depending on the value of the external field. We have shown that the generalized complex-classical approach excludes these catastrophes, which allows one to organize continuous parallel computing on the whole region of values of the external field including critical points. A new representation of the partition function is suggested based on these investigations. Being opposite to the usual definition, it is a complex function and its derivatives are everywhere defined, including at critical points.     

Peculiarities of the rotational dynamics of an ensemble of diatomic homonuclear molecules in a strong laser field

The rotational dynamics of an ensemble of molecules in a laser field has been studied. The results obtained within the framework of the quantum-mechanical and classical approaches have been compared. The features of the rotational dynamics connected with the non-classical character of the system have been described. It was taken into account that before the interaction with a laser pulse the ensemble was in a thermodynamically equilibrium mixed state. The case of an ultrashort laser pulse has been considered as well.