An efficient self-optimized sampling method for rare events in nonequilibrium systems

Rare events such as nucleation processes are of ubiquitous importance in real systems.The most popular method for nonequilibrium systems,forward flux sampling(FFS),samples rare events by using interfaces to partition the whole transition process into sequence of steps along an order parameter connecting the initial and final states.FFS usually suffers from two main difficulties:low computational efficiency due to bad interface locations and even being not applicable when trapping into unknown intermediate metastable states.In the present work,we propose an approach to overcome these difficulties,by self-adaptively locating the interfaces on the fly in an optimized manner.Contrary to the conventional FFS which set the interfaces with equal distance of the order parameter,our approach determines the interfaces with equal transition probability which is shown to satisfy the optimization condition.This is done by firstly running long local trajectories starting from the current interface i to get the conditional probability distribution Pc(>i|i),and then determining i+1by equaling Pc(i+1|i)to a give value p0.With these optimized interfaces,FFS can be run in a much more efficient way.In addition,our approach can conveniently find the intermediate metastable states by monitoring some special long trajectories that neither end at the initial state nor reach the next interface,the number of which will increase sharply from zero if such metastable states are encountered.We apply our approach to a two-state model system and a two-dimensional lattice gas Ising model.Our approach is shown to be much more efficient than the conventional FFS method without losing accuracy,and it can also well reproduce the two-step nucleation scenario of the Ising model with easy identification of the intermediate metastable state.

Nonequilibrium work equalities in isolated quantum systems

We briefly introduce the quantum Jarzynski and Bochkov-Kuzovlev equalities .in isolated quantum Hamiltonian sys- tems, including their origin, their derivations using a quantum Feynman-Kac formula, the quantum Crooks equality, the evolution equations governing the characteristic functions of the probability density functions for the quantum work, and recent experimental verifications. Some resultsare given here for the first time. We particularly emphasize the formally structural consistence between these quantum equalities and their classical counterparts, which are useful for understanding the existing equalities and pursuing new fluctuation relations in other complex quantum systems.

Unifying quantum heat transfer and superradiant signature in a nonequilibrium collective-qubit system:A polaron-transformed Redfield approach

We investigate full counting statistics of quantum heat transfer in a collective-qubit system constructed by multiqubits interacting with two thermal baths. The nonequilibrium polaron-transformed Redfield approach embedded with an auxiliary counting field is applied to obtain the steady state heat current and fluctuations, which enables us to study the impact of the qubit–bath interaction in a wide regime. The heat current, current noise, and skewness are all found to clearly unify the limiting results in the weak and strong couplings. Moreover, the superradiant heat transfer is clarified as a system-size-dependent effect, and large number of qubits dramatically suppress the nonequilibrium superradiant signature.

The nonequilibrium phase transition and the symmetry revival induced by time delay in an asymmetric bistable system with correlated noises

The nonequilibrium phase transition and the symmetry revival induced by time delay in a bistable system are investigated. The stationary probability distribution function （SPDF） of the bistable system with time delay and correlated noises are calculated by an analytical method and stochastic simulation respectively. The analytical and simulative results indicate that： （1） There is a certain value of λ（λ denotes the strength of correlations between the multiplicative and additive noises） to make the SPDF symmetric under some time delay; however, above or below the given value, the symmetry will be broken; （2） With the monotonic change of λ, the unimodal peak structure of SPDF becomes bimodal at the beginning, then it becomes unimodal again; this means that there is a reentrance phenomenon in the process; （3） There is a critical value of delay time, which makes the lower peak of SPDF equal to the higher one under the critical condition. This means that the symmetry revival phenomenon emerges.

Nonequilibrium free energy and information flow of a double quantum-dot system with Coulomb coupling

We build a double quantum-dot system with Coulomb coupling and aim at studying connections among the entropy production,free energy,and information flow.By utilizing concepts in stochastic thermodynamics and graph theory analysis,Clausius and nonequilibrium free energy inequalities are built to interpret local second law of thermodynamics for subsystems.A fundamental set of cycle fluxes and affinities is identified to decompose two inequalities by using Schnakenberg's network theory.Results show that the thermodynamic irreversibility has energy-related and information-related contributions.A global cycle associated with the feedback-induced information flow would pump electrons against the bias voltage,which implements a Maxwell demon.

Quantum speed limits of a qubit system interacting with a nonequilibrium environment

The speed of evolution of a qubit undergoing a nonequilibrium environment with spectral density of general ohmic form is investigated. First we reveal non-Markovianity of the model, and find that the non-Markovianity quantified by information backflow of Breuer et al. [Phys. Rev. Lett. 103 210401（2009）] displays a nonmonotonic behavior for different values of the ohmicity parameter s in fixed other parameters and the maximal non-Markovianity can be achieved at a specified value s. We also find that the non-Markovianity displays a nonmonotonic behavior with the change of a phase control parameter. Then we further discuss the relationship between quantum speed limit（QSL） time and non-Markovianity of the open-qubit system for any initial states including pure and mixed states. By investigation, we find that the QSL time of a qubit with any initial states can be expressed by a simple factorization law： the QSL time of a qubit with any qubitinitial states are equal to the product of the coherence of the initial state and the QSL time of maximally coherent states,where the QSL time of the maximally coherent states are jointly determined by the non-Markovianity, decoherence factor and a given driving time. Moreover, we also find that the speed of quantum evolution can be obviously accelerated in the wide range of the ohmicity parameter, i.e., from sub-Ohmic to Ohmic and super-Ohmic cases, which is different from the thermal equilibrium environment case.

Entropy Production along Dominant Pathway of Nonequilibrium Phase Transition in Mesoscopic Chemical System

We consider a bistable mesoscopic chemical reaction system and calculate entropy produc- tion along the dominant pathway during nonequilibrium phase transition. Using probability generating function method and eikonal approximation, we first convert the chemical master equation into the classical Hamilton-Jacobi equation, and then find the dominant pathways between two steady states in the phase space by calculating zero-energy trajectories. We find that entropy productions are related to the actions of the forward and backward dominant pathways. At the coexistence point where the stabilities of the two steady states are equiv alent, both the system entropy change and the medium entropy change are zero; whereas at non-coexistence point both of them are nonzero.

Impact of counter-rotating-wave term on quantum heat transfer and phonon statistics in nonequilibrium qubit–phonon hybrid system

Counter-rotating-wave terms(CRWTs)are traditionally viewed to be crucial in open small quantum systems with strong system–bath dissipation.Here by exemplifying in a nonequilibrium qubit–phonon hybrid model,we show that CRWTs can play the significant role in quantum heat transfer even with weak system–bath dissipation.By using extended coherent phonon states,we obtain the quantum master equation with heat exchange rates contributed by rotating-waveterms(RWTs)and CRWTs,respectively.We find that including only RWTs,the steady state heat current and current fluctuations will be significantly suppressed at large temperature bias,whereas they are strongly enhanced by considering CRWTs in addition.Furthermore,for the phonon statistics,the average phonon number and two-phonon correlation are nearly insensitive to strong qubit–phonon hybridization with only RWTs,whereas they will be dramatically cooled down via the cooperative transitions based on CRWTs in addition.Therefore,CRWTs in quantum heat transfer system should be treated carefully.

A polaron theory of quantum thermal transistor in nonequilibrium three-level systems

We investigate the quantum thermal transistor effect in nonequilibrium three-level systems by applying the polarontransformed Redfield equation combined with full counting statistics.The steady state heat currents are obtained via this unified approach over a wide region of system–bath coupling,and can be analytically reduced to the Redfield and nonequilibrium noninteracting blip approximation results in the weak and strong coupling limits,respectively.A giant heat amplification phenomenon emerges in the strong system–bath coupling limit,where transitions mediated by the middle thermal bath are found to be crucial to unravel the underlying mechanism.Moreover,the heat amplification is also exhibited with moderate coupling strength,which can be properly explained within the polaron framework.

Oscillatory Shannon entropy in the process of equilibration of nonequilibrium crystalline systems

We present a study of the equilibration process of some nonequilibrium crystalline systems by means of molecular dynamics simulation technique. The nonequilibrium conditions are achieved in the systems by randomly defining velocity components of the constituent atoms. The calculated Shannon entropy from the probability distribution of the kinetic energy among the atoms at different instants during the process of equilibration shows oscillation as the system relaxes towards equilibrium. Fourier transformations of these oscillating Shannon entropies reveal the existence of Debye frequency of the concerned system.

Nonequilibrium Statistical Modeling of Fatigue Crack Growth Behaviour

In order to study the influence of microstructural texture on the growth of short fatigue cracks in metals, the nonequilibrium statistical theory of fatigue fracture correlating a microscopic mechanism with the macroscopic properties is modified to take into consideration the microstructural features of a material, thereby allowing a rationalisation of the experimental data of short fatigue crack growth and long fatigue crack growth. The nonequilibrium statistical theory thus developed relates the growth of cracks with a dislocation mechanism to simulate short fatigue crack growth with the long fatigue crack growth behaviour and predicts the fatigue crack growth rates throughout the fatigue lifetime. The results is finally compared with that of other fatigue theories.

Nonequilibrium Statistical Theory of Fracture

Nonequilibrium statistical theory of fracture is a theory of fracture that macromechanical quantities can be derived from the microscopic atomic mechanism of microcrack(or microvoid)evolution kinetcs by means of nonequilibrium statistical physical concepts and methods. The microcrack evolution equation is the central equation in the theory.The coefficents of the equation, the microcrack growth rate and the microcrack nucleation rate,come from microscopic atomic mechanism.The solution of the equation connects with macromechanical quantities by the model of the weakest chain. All the other formulas and quantities, for instance, distribution function,fracture probability, reliability, failure rate and macromechanical quantities such as strength, toughness, life etc. and their statistical distribution function and statistical fluctuation are derived in a unified fashion and expressed by a few physical parameters. This theory can be widely applied to various kinds of fracture, such as the brittle, fatigue, delayed and environmental fracture of metals and structural ceramics. The theoretical framework of this theory is given in this paper.

Spectral Shift of π→π^＊ Transition for p-Nitroaniline Based on a New Expression of Nonequilibrium Solvation Energy

According to the nonequilibrium solvation theory studies, a constrained equilibrium principle is introduced and applied to the derivations of the nonequilibrium solvation energy, and a reasonable expression of the spectral shift of the electronic absorption spectra is deduced. Furthermore, the lowest transition of p-nitroaniline （pNA） in water is investigated by time-dependent density functional theory method. In addition, the details of excited state properties of pNA are discussed. Using our novel expression of the spectral shift, the value of -0.99 eV is obtained for π→π^＊ transition in water, which is in good agreement with the available experimental result of -0.98 eV.

Numerical Study of High-Temperature Nonequilibrium Flow around Reentry Vehicle Coupled with Thermal Radiation

Accurate aerodynamic heating prediction is of great significance to current manned space flight and deep space exploration missions.The temperature in the shock layer surrounding the reentry vehicle can reach up to 10,000 K and result in remarkable thermochemical nonequilibrium,as well as considerable radiative heat transfer.In general,high-temperature flow simulations coupled with thermal radiation require appropriate numerical schemes and physical models.In this paper,the equations governing hypersonic nonequilibrium flow,based on a three-temperature model combined with a thermal radiation solving approach,are used to investigate the radiation effects in the reentry shock layer.An axisymmetric spherical case shows that coupling the flow-field simulation with radiation has a scarce influence on the convective heating prediction,but has some impact on the radiative heating calculation.In particular,for the Apollo capsule reentry,both the absorption coefficient and incident radiation are remarkable inside the shock layer.The radiative heating maximum reaches nearly 38%of that of the convective heating making a considerable contribution to the total aerodynamic heating.These results indicate that in the hypersonic regime,in order to account for the total heating,it is necessary to simulate the high-temperature thermochemical nonequilibrium flows coupled with thermal radiation.

Integrated system of comprehensive utilizing the concentrated brine of Yuncheng salt-lake basing on salt-forming diagram

The comprehensive utilization and environment-friendliness of processes for recovering fresh water or valuable salt from seawater, salt-lakes, or mineral deposits are of utmost importance for sustainable development.One primitive sustainable process for recovering salt from sodium-sulfate-type brine in Yuncheng salt lake had been considered one of the greatest inventions of ancient China, however, the replaced process of mass extraction of single Na_2SO_4 in recent years, has reduced a large amount of residual brine.In this research, relying on the salt-forming diagram in the non-equilibrium state, the technical secrets of ancient salt processes were uncovered, and a new comprehensive utilization system was proposed and tested experimentally.The new system includes a vacuum salt-making process and a normal pressure kieserite process, which can gradually eliminate the existed waste liquid and aid in the sustainable development of the Yuncheng salt-lake.The continuous experiment of salt-making process running stably in the double salt region without double salt formation, which proves the feasibility of salt-forming diagram applied in industrial process.Thus salt-forming diagram would be extremely valuable to industry process design and control, especially, the treatment of concentrated brine.

Numerical modeling of radionuclide migration in porous media with nonequilibrium sorption

When radionuclides migrate in porous media with water serving as carrier, the mechanism of sorption and desorption is not negligible. nonequilibrium conditions exist in sorption and desorption. In this paper,a numerical model of radionuclide migration with nonequilibrium sorption was developed.The algorithm of numerical descretizing and direct substituting was adopted in coupling of the convective-dispersive equation and the nonequilibrium sorption isotherm in this model ,and this makes it easier to solve the model numerically.A quantitative analysis is made for the first time that the influence of nonequilibrium sorption, represented by the rate coefficient which shows how quickly the nonequilibrium condition in sorption and desorption reaches equilibrium on the migration of radionuclide,and results show that it affects the migration perceptibly. Finally the model was verified by using the observed data of radionuclide migration test conducted in the field, and which clarified its availability.

Interface of solid steel and liquid aluminum under nonequilibrium diffusion

The nonequilibrium diffusion of liquid aluminum atoms in cross direction in the innerpart of the solid steel base has been realized by using methods such as roughening steel plate surface, immersing flux on steel plate surface and short time diffusion, and the interface of solid steel and liquid aluminum under nonequilibrium diffusion in cross direction was formed by using rapid solidification. The interfacial structure was studied by means of electron probe microanalysis. The results showed that the interfacial structure of solid steel and liquid aluminum under nonequilibrium diffusion in cross direction is quite different from that of solid steel and liquid aluminum under conventional diffusion, that is, the interface of solid steel and liquid aluminum under nonequilibrium diffusion in cross direction is made up of groups of Al 13 Fe 4 teeth (which grew from the contact surface to steel base inner) at the bulges of steel plate surface and Fe Al solid solution (whose Al content is less than 3.5%) at the concaves of steel plate surface between the groups of Al 13 Fe 4 teeth.

Heat Generation by Electric Current in Normal-Metal-Molecular Quantum Dot-Superconductor System

We investigate the heat generation induced by electrical current in a normal-metal-molecular quantum dot-superconductor （NDS） system. By using nonequilibrium Green＇s function method, the heat generation Q is derived and studied in detail. The superconducting lead influences the heat generation significantly. An obvious step appears in Q - eV characteristics and the iocation of this step is related with the phonon frequency ωo. The heat generations exhibit very different behaviour in the condition eV 〈 △ and eV 〉 △ due to different tunneling mechanism. From the study of Q - eVg curves, there is an extra peak as eV 〉 △. The difference in this two cases is also shown in Q - ωo curve, an extra peak emerges as eV 〉 △.

The Stepping Motion of Brownian Particle Derived by Nonequilibrium Fluctuation

The direct motion of Brownian particle is considered as a result of system derived by external nonequilibriumfluctuating. The cooperative effects caused by asymmetric ratchet potential, external rocking force and additive colorednoise drive a Brownian particle in the directed stepping motion. This provides this kind of motion of kinesin along amicrotubule observed in experiments with a reasonable explanation.

Thermochemical Nonequilibrium 2D Modeling of Nitrogen Inductively Coupled Plasma Flow

Two-dimensional（2D） numerical simulations of thermochemical nonequilibrium inductively coupled plasma（ICP） flows inside a 10-kW inductively coupled plasma wind tunnel（ICPWT） were carried out with nitrogen as the working gas.Compressible axisymmetric NavierStokes（N-S） equations coupled with magnetic vector potential equations were solved.A fourtemperature model including an improved electron-vibration relaxation time was used to model the internal energy exchange between electron and heavy particles.The third-order accuracy electron transport properties（3rd AETP） were applied to the simulations.A hybrid chemical kinetic model was adopted to model the chemical nonequilibrium process.The flow characteristics such as thermal nonequilibrium,inductive discharge,effects of Lorentz force were made clear through the present study.It was clarified that the thermal nonequilibrium model played an important role in properly predicting the temperature field.The prediction accuracy can be improved by applying the 3rd AETP to the simulation for this ICPWT.