Benford’s law in non-equilibrium processes: Droplet collisions case

Benford’s law is investigated for the simulation results generated from non-equilibrium molecular dynamics. A statistic to measure how closely a set of the numbers follows Benford’s law is defined. The simulation data are from the collisions of two nano droplets with different impact velocities. When a non-equilibrium system returns to its equilibrium state, some physical quantities relevant to the non-equilibrium settings follow Benford’s law more closely. The initial settings for the non-equilibrium state can be interpreted as a data fabrication of its corresponding equilibrium state. A connection with the Shannon entropy for the first digit distribution is also discussed.     

Relativistic heavy-ion collisions: An approach based on non-equilibrium thermodynamics

A new theory of particle production in high energy collisions is proposed which is based on non-equilibrium thermodynamics. The non-equilibrium model is a major extension of the equilibrium thermodynamic model of relativistic heavy-ion collisions developed earlier. While the equilibrium thermodynamic theory is appropriate for the formation of light nuclei and for pions, the non-equilibrium theory applies to the creation of particles heavier than the pion, which include such particles as the strange mesons, strange baryons and the anti-nucleons. Using an approach based on the degree of the reaction of kinetic theory, the time evolution of the composition of hadronic systems in incomplete equilibrium is investigated. Densities of produced particles are related to space-time quantities and to the production cross sections of the underlying dynamic processes. An application of the non-equilibrium approach to the production of strange matter is given. The importance of secondary processes, following pion production, in the formation of strange matter is shown. In fact, the secondary production process for kaons is as important as the direct production process arising from initial nucleon-nucleon (NN) collision of a first collision picture. Thus, kaons can be produced in a late stage of the collision of two nuclei and they do not necessarily reflect the early stages of the collision as first thought. Using the experimental number of kaons, the time of reaction is also estimated. No evidence for a long-lived state of the nuclear system is found. Expressions for particle production ratios are developed. The results of an equilibrium theory and a non-equilibrium theory are found to be similar for such ratios. The chemical equilibrium constant is shown to be present in the non-equilibrium theory; the Boltzmann factor in the production threshold energy appears in the equilibrium theory. The K^?/K⁺ ratio is estimated. Surprisingly, reasonable agreement with experiment is found in the K^?/K⁺ ratio using the equilibrium theory, even though the production processes for K⁺'s and K^?'s treated individually, are not ones for which the equilibrium theory applies. It is shown that a fundamental difference between the equilibrium and non-equilibrium theory is lost when particle ratios for non-equilibrium particles are taken. Expressions for the production of complex composite structures made of strange particles are developed. The non-equilibrium model with some modifications may be useful for high energy NN and pion-nucleon collisions.     

Mesoscopic Modeling for Continuous Spin Lattice Systems: Model Problems and Micromagnetics Applications

In this paper we derive deterministic mesoscopic theories for model continuous spin lattice systems both at equilibrium and non-equilibrium in the presence of thermal fluctuations. The full magnetic Hamiltonian that includes singular integral (dipolar) interactions is also considered at equilibrium. The non-equilibrium microscopic models we consider are relaxation-type dynamics arising in kinetic Monte Carlo or Langevin-type simulations of lattice systems. In this context we also employ the derived mesoscopic models to study the relaxation of such algorithms to equilibrium     

Non-equilibrium 2PI potential and its possible application to evaluation of bulk viscosity

Within non-equilibrium Green’s function technique on the real-time contour and the two-particle irreducible Φ-functional method, a non-equilibrium potential is introduced. It naturally generalizes the conventional thermodynamic potential with which it coincides in thermal equilibrium. Variations of the non-equilibrium potential over respective parameters result in the same quantities as those of the thermodynamic potential but in arbitrary non-equilibrium. In particular, for slightly non-equilibrium inhomogeneous configurations a variation of the non-equilibrium potential over volume is associated with the trace of the non-equilibrium stress tensor. The latter is related to the bulk viscosity. This provides a novel way for evaluation of the bulk viscosity.     

Free energy landscape from path-sampling: application to the structural transition in LJ38

We introduce a path-sampling scheme that allows equilibrium state-ensemble averages to be computed by means of a biased distribution of non-equilibrium paths. This non-equilibrium method is applied to the case of the 38-atom Lennard-Jones atomic cluster, which has a double-funnel energy landscape. We calculate the free energy profile along the Q₄ bond orientational order parameter. At high or moderate temperature the results obtained using the non-equilibrium approach are consistent with those obtained using conventional equilibrium methods, including parallel tempering and Wang-Landau Monte Carlo simulations. At lower temperatures, the non-equilibrium approach becomes more efficient in exploring the relevant inherent structures. In particular, the free energy agrees with the predictions of the harmonic superposition approximation.     

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.     

汽液界面动力学行为与热力学性质的分子动力学研究

本文采用分子动力学方法研究了热平衡条件下的汽液界面的动力学行为和热力学性质。统计获得了界面区的密度、压力张量及温度的分布,并且从分子层次观察分析了界面结构和动力学特性。研究表明汽液界面是一个随时间起伏涨落的曲面,界面层的分子并不是处于液相和蒸汽相之间的一种过渡状态,从汽相到液相密度的连续变化是长时间的统计结果,汽渡过渡区的厚度与汽液界面区的密度涨落的范围是一致的。对于平衡条件下的汽液界面,由于汽液相变的影响,在紧贴界面处存在一个分子平均动能非平衡分布的区域。此非平衡区域的存在与汽液两相的宏观热平衡并不矛盾,但可能对蒸发／凝结流率的估计有不可忽略的影响。     

Inequalities for Non-equilibrium Fluctuations of Work

Five previously unknown inequalities relating equilibrium free energy differences and non-equilibrium work fluctuations are derived, and lucid path to derivation of many similar inequalities is presented. These results are based upon combined exploitation of the Jarzynski equality and the generalization of the scheme for producing uncertainty-type inequalities due to H. Weyl. The inequalities may possibly lead to better understanding of behavior of the equilibrium free-energy estimators from non-equilibrium experimental data in many important applications concerning biological, chemical, and physical molecular processes.     

Electronic cooling in superconducting tunnel junctions

The cooling power provided by the current through a superconductor/insulator/superconductor tunnel junction is studied theoretically. The influence of non-equilibrium distributions of the quasi-particles on the heat flow is analysed within a simple relaxation model. A superconducting gap enhancement can be explained within the equilibrium as well as the non-equilibrium model.     

低压汽轮机三维叶栅通道内湿蒸汽两相流动的数值模拟与分析

采用完全气体单相流动模型、实际气体平衡态凝结和非平衡态自发凝结三种不同的计算方法对某低压汽轮机静叶栅中三维湿蒸汽两相流动进行了模拟和分析.计算表明:三种模式计算结果有一定的差别;水滴的生长过程对出口气流角分布有一定的影响;非平衡态计算得到的出口湿度比平衡态计算结果略微小一些;进一步的分析表明在非平衡态计算中,进口水滴半径对出口湿度和出口水滴半径均有影响.     

Compression behavior of elastomeric networks-non-equilibrium effects

The compression behavior of some rubberlike networks in equilibrium and non-equilibrium conditions has been investigated. The experimental data clearly indicate that non-equilibrium components are operative on the compression modulus value. Results are interpreted in terms of supramolecular order in the amorphous materials.     

Theoretical Computation for Non-Equilibrium Air Plasma Electrical Conductivity at Atmospheric Pressure

Based on the Chapman-Enskog theory, we calculate the electrical conductivity of non-equilibrium air plasma in the two-temperature model. We consider different degrees of non-equilibrium, which is defined by the ratio of electronic temperature to heavy particles temperature. The method of computing the composition of air plasma is demonstrated. After calculating the electrical conductivity from electron temperature 1000 K to 15000K, the present result is compared with Murphy＇s study [Plasma Chem. Plasma Process 15 （1994） 279] for equilibrium case. All the calculation is completed at atmospheric pressure. The present results may have potential applications in numerical calculation of non-equilibrium air plasma.     

Discussions on the non-equilibrium effects in the quantitative phase field model of binary alloys

All the quantitative phase field models try to get rid of the artificial factors of solutal drag,interface diffusion and interface stretch in the diffuse interface.These artificial non-equilibrium effects due to the introducing of diffuse interface are analysed based on the thermodynamic status across the diffuse interface in the quantitative phase field model of binary alloys.Results indicate that the non-equilibrium effects are related to the negative driving force in the local region of solid side across the diffuse interface.The negative driving force results from the fact that the phase field model is derived from equilibrium condition but used to simulate the non-equilibrium solidification process.The interface thickness dependence of the non-equilibrium effects and its restriction on the large scale simulation are also discussed.     

A correlation measure in non-equilibrium phase transitions

Bit-number cumulants of a probability distribution give ordered measures of correlations between subsystems. Especially the second one, the bit-number variance (which in equilibrium is connected with specific heat) is discussed with respect to its critical behaviour for special non-equilibrium phase transitions in chemical reaction systems. Also in non-equilibrium the critical behaviour indicates critical correlations.     

Population trapping and inversion in ultracold Fermi gases by excitation of the optical lattice: non-equilibrium Floquet–Keldysh description

A gas of ultracold interacting quantum degenerate Fermions is considered in a three-dimensional optical lattice which is externally modulated in the frequency and the amplitude. This theoretical study utilizes the Keldysh formalism to account for the system being out of thermodynamical equilibrium. A dynamical mean field theory, extended to non-equilibrium, is presented to calculate characteristic quantities such as the local density of states and the non-equilibrium distribution function. A dynamic Franz–Keldysh splitting is found which accounts for the non-equilibrium modification of the underlying bandstructure. The found characteristic Floquet-fan like bandstructure accounts for the quantized nature of the effect over all frequency space.     

Criticality in a non-equilibrium,driven system: Charged colloidal rods (fd-viruses) in electric fields

Experiments on suspensions of charged colloidal rods (fd-virus particles) in external electric fields are performed, which show that a non-equilibrium critical point can be identified. Several transition lines of field-induced phases and states meet at this point and it is shown that there is a length- and time-scale which diverge at the non-equilibrium critical point. The off-critical and critical behavior is characterized, with both power law and logarithmic divergencies. These experiments show that analogous features of the classical, critical divergence of correlation lengths and relaxation times in equilibrium systems are also exhibited by driven systems that are far out of equilibrium, related to phases/states that do not exist in the absence of the external field.     

Narrow-band model for nonequilibrium air plasma radiation

A band model is developed for the prediction of radiative transfer in air plasma applications under equilibrium and non-equilibrium conditions. For non-equilibrium applications, the medium is described by rotational–translational and vibrational temperatures but the populations of electronic states can be arbitrary. A specific formulation of the statistical narrow-band (SNB) model is developed for optically thick electronic systems of diatomic molecules when their populations are described by an electronic temperature. Model parameters, deduced from line by line calculations in the Voigt regime, are shown to be also convenient for arbitrary distribution of molecular electronic populations. This model is then complemented to include optically thin electronic systems and the continuum radiation through the simple box model, and line by line calculations for atomic lines. Several tests including equilibrium, non-equilibrium, uniform, and non-uniform conditions show the ability of this hybrid model to provide accurate and efficient solutions for radiative transfer problems in air plasmas.     

The second-order dynamic phase transition and Lee--Yang zeros in Eggers urn model

A second-order dynamic phase transition in a non-equilibrium Eggers urn model for the separation of sand is studied. The order parameter, the susceptibility and the stationary probability distribution have been calculated. By applying the Lee-Yang zeros method of equilibrium phase transitions, we study the distributions of the effective partition function zeros and obtain the same result for the model. Thus, the Lee-Yang theory can be applied to a more general non-equilibrium system.