Quantum Macrostatistical Picture of Nonequilibrium Steady States

We apply our quantum macrostatistical treatment of irreversible processes to prove that, in nonequilibrium steady states, (a) the hydrodynamical observables execute a generalised Onsager–Machlup process and (b) the spatial correlations of these observables are generically of long range. The key assumptions behind these results are a nonequilibrium version of Onsager regression hypothesis, together with certain hypotheses of chaoticity and local equilibrium for hydrodynamical fluctuations.     

Representation of Nonequilibrium Steady States in Large Mechanical Systems

Recently a novel concise representation of the probability distribution of heat conducting nonequilibrium steady states was derived. The representation is valid to the second order in the “degree of nonequilibrium”, and has a very suggestive form where the effective Hamiltonian is determined by the excess entropy production. Here we extend the representation to a wide class of nonequilibrium steady states realized in classical mechanical systems where baths (reservoirs) are also defined in terms of deterministic mechanics. The present extension covers such nonequilibrium steady states with a heat conduction, with particle flow (maintained either by external field or by particle reservoirs), and under an oscillating external field. We also simplify the derivation and discuss the corresponding representation to the full order.     

Phase separation dynamics in driven diffusive systems

We study phase separation dynamics in a driven diffusive system. Our simulations are based on the Cahn-Hilliard equation with an additional flux term due to an external field. We study the dynamical scaling parallel and perpendicular to the field. A crossover is observed from isotropic domains at early times to extremely anisotropic domains at later times. We find that the inverse interfacial density (an isotropic measure of the domain size) increases ast , with =1/3, from early times independent of the field strength, even though we do not observe dynamical scaling during these times. Our results indicate that a growth exponent =1/3 may be more universal than previously expected. We analyze the dynamics in terms of surface driven instabilities and one-dimensional solitary waves.     

Steady state in two-dimensional diffusion-controlled reactions

We investigate the conditions under which a steady state can be reached in a two-dimensional diffusion-controlled trapping reaction. If there is no interaction between trap and diffusing particles, the reaction rate decreases monotonically to zero. Here we show that a logarithmic attractive potential between trap and diffusing particles leads to a finite steady-state reaction rate. A steady state can also be reached if the diffusing particles move under the action of a uniform external field. More unexpectedly, a steady-state rate can be obtained in the absence of any “assisting field” if the trap grows due to the absorption of the diffusing particles. The reaction rates are calculated in all cases.     

Interfacial growth in driven Ginzburg-Landau models: Short and long-time dynamics

Interfacial growth in driven systems is studied from the initial stage to the longtime regime. Numerical integrations of a Ginzburg-Landan type equation with a new flux term introduced by an external field are presented. The interfacial instabilities are induced by the external field. From the numerical results, we obtain the dispersion relation for the initial growth. During the intermediate temporal regime, fingers of a characteristic triangular shape could grow. Depending on the boundary conditions, the final state corresponds to strips, multifinger states, or a one-finger state. The results for the initial growth are interpreted by means of surface-driven and Mullins-Sekerka instabilities. The shape of the one-finger state is explained in terms of the characteristic length introduced by the external field.     

Steady State Thermodynamics

The present paper reports our attempt to search for a new universal framework in nonequilibrium physics. We propose a thermodynamic formalism that is expected to apply to a large class of nonequilibrium steady states including a heat conducting fluid, a sheared fluid, and an electrically conducting fluid. We call our theory steady state thermodynamics (SST) after Oono and Paniconi's original proposal. The construction of SST is based on a careful examination of how the basic notions in thermodynamics should be modified in nonequilibrium steady states. We define all thermodynamic quantities through operational procedures which can be (in principle) realized experimentally. Based on SST thus constructed, we make some nontrivial predictions, including an extension of Einstein's formula on density fluctuation, an extension of the minimum work principle, the existence of a new osmotic pressure of a purely nonequilibrium origin, and a shift of coexistence temperature. All these predictions may be checked experimentally to test SST for its quantitative validity.     

Theory on Morphological Instability in Driven Systems

Motivated by recent findings from simulation of a driven lattice gas under shifted periodic boundary conditions, we study within the context of a continuum model the interfacial stability of driven diffusive systems. In this model, an external driving field maintains the system away from equilibrium. Well below criticality, steady-state solutions of the associated bulk kinetic equation are obtained. Our results successfully account for the novel features found in simulation. In particular, the solution describing a pair of interfaces tilted with respect to the driving field under periodic boundary conditions shows a tilt-dependent bulk density (and internal energy), and boundary layers near one of the interfaces. Focusing on the interface dynamics, one finds that such an interface exhibits a characteristic Mullins-Sekerka instability. This is argued to be responsible for the onset of the single- to multistrip transformation observed in simulation.     

Steady state investigation on neutronics of a molten salt reactor considering the flow effect of fuel salt

The Molten Salt Reactor (MSR),one of the‘Generation Ⅳ'concepts,is a liquid-fuel reactor,which is different from the conventional reactors using solid fissile materials due to the flow effect of fuel salt.The study on its neutronice considering the fuel salt flow,which is the base of the thermal-hydraulic calculation and safety analysis,must be done.In this paper,the theoretical model on neutronics under steady condition for a single-liquid-fueled MSR is conducted and calculated by numerical method.The neutronics model consists of two group neutron diffusion equations for fast and thermal neutron fluxes,and balance equations for six-group delayed neutron precursors considering the flow effect of fuel salt. The spatial discretization of the above models is based on the finite volume method,and the discretization equations are computed by the source iteration method.The distributions of neutron fluxes and the distributions of the delayed neutron precursors in the core are obtained.The numerical calculated results show that,the fuel salt flow has little effect on the distribution of fast and thermal neutron fluxes and the effective multiplication factor;however,it affects the distribution of the delayed neutron precursors significantly,especially the long-lived one.In addition,it could be found that the delayed neutron precursors influence the nentronics slightly under the steady condition.     

Steady state investigation on neutronics of a molten salt reactor considering the flow effect of fuel salt

The Molten Salt Reactor (MSR), one of the `Generation IV' concepts, is a liquid-fuel reactor, which is different from the conventional reactors using solid fissile materials due to the flow effect of fuel salt. The study on its neutronics considering the fuel salt flow, which is the base of the thermal-hydraulic calculation and safety analysis, must be done. In this paper, the theoretical model on neutronics under steady condition for a single-liquid-fueled MSR is conducted and calculated by numerical method. The neutronics model consists of two group neutron diffusion equations for fast and thermal neutron fluxes, and balance equations for six-group delayed neutron precursors considering the flow effect of fuel salt. The spatial discretization of the above models is based on the finite volume method, and the discretization equations are computed by the source iteration method. The distributions of neutron fluxes and the distributions of the delayed neutron precursors in the core are obtained. The numerical calculated results show that, the fuel salt flow has little effect on the distribution of fast and thermal neutron fluxes and the effective multiplication factor; however, it affects the distribution of the delayed neutron precursors significantly, especially the long-lived one. In addition, it could be found that the delayed neutron precursors influence the neutronics slightly under the steady condition.     

Driven nonequilibrium lattice systems with shifted periodic boundary conditions

We present the first study of a driven nonequilibrium lattice system in the two-phase region, withshifted periodic boundary conditions, forcing steps into the interface. When the shift corresponds to small angles with respect to the driving field, we find nonanalytic behavior in the (internal) energy of the system, supporting numerical evidence that interface roughness is suppressed by the field. For larger shifts, the competition between the driving field and the boundary induces the breakup of a single strip with tilted interfaces into many narrower strips with aligned interfaces. The size and temperature dependences of the critical angles of such breakup transitions are studied.     

双色噪声激励下FHN神经元系统的稳态性质

应用统一色噪声理论研究了双色噪声激励下一维FitzHugh-Nagumo (FHN)神经元系统的动力学性质,即稳态概率分布函数和其平均值. 给出了FHN神经元系统的稳态概率密度和平均值的解析表达式. 结果表明: 乘性噪声的自关联时间τ ₁、加性噪声的自关联时间τ ₂、加性噪声强度α 和乘性噪声强度D都能够诱导非平衡相变的产生. α和D的增大有利于系统从激发态向静息态转换. τ₁, τ₂的增大有利于系统从静息态向激发态转换. 噪声强度和其自关联时间的作用完全相反.     

Comments on the Entropy of Nonequilibrium Steady States

We discuss the entropy of nonequilibrium steady states. We analyze the so-called spontaneous production of entropy in certain reversible deterministic nonequilibrium system, and its link with the collapse of such systems towards an attractor that is of lower dimension than the dimension of phase space. This means that in the steady state limit, the Gibbs entropy diverges to negative infinity. We argue that if the Gibbs entropy is expanded in a series involving 1, 2,... body terms, the divergence of the Gibbs entropy is manifest only in terms involving integrals whose dimension is higher than, approximately, the Kaplan–Yorke dimension of the steady state attractor. All the low order terms are finite and sum in the weak field limit to the local equilibrium entropy of linear irreversible thermodynamics.     

Einstein Relation for Nonequilibrium Steady States

The Einstein relation, relating the steady state fluctuation properties to the linear response to a perturbation, is considered for steady states of stochastic models with a finite state space. We show how an Einstein relation always holds if the steady state satisfies detailed balance. More generally, we consider nonequilibrium steady states where detailed balance does not hold and show how a generalisation of the Einstein relation may be derived in certain cases. In particular, for the asymmetric simple exclusion process and a driven diffusive dimer model, the external perturbation creates and annihilates particles thus breaking the particle conservation of the unperturbed model.     

Steady state Behaviour of a Three level Ladder Atomic System with Incoherent Population Pumping in a Squeezed Vacuum

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Steady state and time resolved laser-induced fluorescence of garlic plants treated with titanium dioxide nanoparticles

The study involves investigation of the effect of the interaction of titanium dioxide nanoparticles with garlic plant by spectroscopy techniques. For this, garlic plants have been grown in the laboratory under controlled conditions of light flux, temperature, humidity, and nutrient media. The growth and biomass parameters in terms of shoot length, fresh, and dry mass are found to increase upon the treatment of titanium dioxide nanoparticles while a reduction is observed in the root length of the garlic plants. The steady state laser-induced fluorescence, time resolved laser-induced fluorescence, and ultraviolet visible spectra of the control and titanium dioxide nanoparticles-treated plants have been acquired. The curve fitting data reveal that titanium dioxide nanoparticles decrease the intensity and fluorescence intensity ratio of red and far red chlorophyll fluorescence bands indicating increase in the photosynthetic activity and chlorophyll content. The evaluation of life time of the excited chlorophyll molecule shows that life time is effected by the treatment of the titanium dioxide nanoparticles. The results pertaining to ultraviolet visible measurement indicate increase in the concentration of chlorophyll a, chlorophyll b, total chlorophyll, carotenoid, and quercetin in the leaves of garlic plants treated with titanium dioxide nanoparticles.     

Field theory of critical behavior in a driven diffusive system

We use a field theoretic renormalization group method to study the critical properties of a diffusive system with a single conserved density subject to a constant uniform external field. A fixed point stable belowd _c=5 is found to govern the critical behavior. Scaling forms of density correlation functions are derived and critical exponents are obtained to all orders in =5–d. Spatial correlations are found to be very anisotropic with elongated correlations along the external field. Long wavelength transverse fluctuations are suppressed completely to yield mean field transverse exponents.     

Factorised steady states and condensation transitions in nonequilibrium systems

Systems driven out of equilibrium can often exhibit behaviour not seen in systems in thermal equilibrium —for example phase transitions in one-dimensional systems. In this talk I will review a simple model of a nonequilibrium system known as the ‘zero-range process’ and its recent developments. The nonequilibrium stationary state of this model factorises and this property allows a detailed analysis of several ‘condensation’ transitions wherein a finite fraction of the constituent particles condenses onto a single lattice site. I will then consider a more general class of mass transport models, encompassing continuous mass variables and discrete time updating, and present a necessary and sufficient condition for the steady state to factorise. The property of factorisation again allows an analysis of the condensation transitions which may occur.     

Perturbation analysis of a stationary nonequilibrium flow generated by an external force

The stationary flow of a gas in a slab under the action of a constant external force parallel to the walls is analyzed in the context of the Bhatnagar-Gross-Krook model kinetic equation. The force produces spatial gradients along the coordinate normal to the walls. By performing a perturbation expansion in powers of the force, we obtain the hydrodynamic fields up to fifth order in the force. Then the velocity distribution function and all its moments are evaluated to third order. The expansion coefficients are polynomials in the space variable of a degree increasing linearly with the expansion order. Although the series expansion is only asymptotic, it shows how the state of the system is modified by a variation of the external force beyond the linear regime.     

Transition state theory: A generalization to nonequilibrium systems with power-law distributions

Transition state theory (TST) is generalized to nonequilibrium systems with power-law distributions. The stochastic dynamics that gives rise to the power-law distributions for the reaction coordinate and momentum is modeled by Langevin equations and corresponding Fokker-Planck equations. It is considered that a system far away from equilibrium does not have to relax to a thermal equilibrium state with Boltzmann-Gibbs distribution, but asymptotically approaches a nonequilibrium stationary state with a power-law distribution. Thus, we obtain a possible generalization of TST rates to nonequilibrium systems with power-law distributions. Furthermore, we derive the generalized TST rate constants for one-dimensional and n-dimensional Hamiltonian systems away from equilibrium, and obtain a generalized Arrhenius rate for systems with power-law distributions.