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.     

Introduction: Self-organization in nonequilibrium chemical systems

The field of self-organization in nonequilibrium chemical systems comprises the study of dynamical phenomena in chemically reacting systems far from equilibrium. Systematic exploration of this area began with investigations of the temporal behavior of the Belousov-Zhabotinsky oscillating reaction, discovered accidentally in the former Soviet Union in the 1950s. The field soon advanced into chemical waves in excitable media and propagating fronts. With the systematic design of oscillating reactions in the 1980s and the discovery of Turing patterns in the 1990s, the scope of these studies expanded dramatically. The articles in this Focus Issue provide an overview of the development and current state of the field.     

Nambu力学系统的Lie对称性及其守恒量

讨论了Nambu力学系统的Lie对称性;建立了系统Lie对称性的确定方程;得到了该对称性引起的守恒量;研究了Lie对称性逆问题. 并以Euler方程为例说明了本文的主要结果. 关键词： Nambu力学系统 Lie对称性 守恒量     

Sensitivity of nonequilibrium systems

Simple mechanisms through which nonequilibrium structures can be influenced by external fields are discussed. It is shown that a very weak gravitational or electric field can have a large influence on selection or creation of structures. In the absence of cooperativity, the influence of a weak field, to the leading order, is characterized by the ratio (E_int/kT), where E_int is the energy of interaction; however, when there is far-from-equilibrium cooperativity, it is shown that the influence of the field is characterized by $\text{(E}{}_{\mathrm{int}}\text{kT)}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}$.     

Stable nonequilibrium of quantum systems

Scientific-Research Radiophysical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 32, No. 4, pp. 436–443, April, 1989.     

Scaling theory for nonequilibrium systems

We develop a general scaling theory of one-dimensional systems withN components having applications to disorder-order-transitions or order-order transitions of non-equilibrium systems, such as lasers, hydrodynamical systems and non-equilibrium chemical reactions. We include both cases of soft and hard modes. Since fluctuations play a decisive role at the transition point, we take fully account of them. We start from general equations of motion which contain nonlinear forces (or rates), diffusion terms and fluctuating forces. These equations depend on external parameters. When linearized around their steady state solutions, the equations allow for stable, marginal or unstable solutions. The solutions near critical points are represented as superpositions of marginal solutions, whose amplitudes are determined by comparing the coefficients of the scaling parameter up to third order. The scaling of the fluctuating forces and, in the case of chemical reactions, their correlation functions are derived in detail.     

Dynamics of nonequilibrium open systems

The dynamics of a nonequilibrium open system is studied by using projection operator techniques. The influence of the environment on the system is examined and the equations of motion for the expectation values of macrovariables of the system are derived. A method to calculate the non-markovian influence terms is proposed which necessitates solving a certain Volterra equation.     

Time-symmetric fluctuations in nonequilibrium systems

For nonequilibrium steady states, we identify observables whose fluctuations satisfy a general symmetry and for which a new reciprocity relation can be shown. Unlike the situation in recently discussed fluctuation theorems, these observables are time-reversal symmetric. That is essential for exploiting the fluctuation symmetry beyond linear response theory. In addition to time reversal, a crucial role is played by the reversal of the driving fields that further resolves the space-time action. In particular, the time-symmetric part in the space-time action determines the second order effects of the nonequilibrium driving.     

Bose-Einstein condensation in nonequilibrium systems

The properties of quantum statistically degenerate systems of Bosons which are created by an external pump field and decay within a finite lifetime are investigated by means of a Green's function treatment. These investigations help to understand the physical properties of such condensed Bose-systems as excitons, excitonic molecules and spin aligned hydrogen atoms. As an example, recent experiments by Hulin et al. on degenerate excitons in Cu₂O are analyzed and a condensate fraction of about 5% is obtained.     

Statistical description of nonequilibrium self-gravitating systems

Self-gravitating systems are non-equilibrium a priori. A new approach is proposed, which employs a non-equilibrium statistical operator that takes account inhomogeneous distribution of particles and temperature. The method involves a saddle-point procedure to find the dominant contributions to the partition function, thus obtaining all thermodynamic parameters of the system. Probable peculiar features in the behavior of the self-gravitating systems are considered for various conditions. The equation of state for self-gravitating systems has been determined. A new length of the statistical instability is obtained for a real gravitational system, as are parameters of the spatially inhomogeneous distribution of particles and temperature.     

Conservative ensembles for nonequilibrium lattice-gas systems

We show how to set up a constant particle ensemble for the steady state of nonequilibrium lattice-gas systems which originally are defined on a constant rate ensemble. We focus on nonequilibrium systems in which particles are created and annihilated on the sites of a lattice and described by a master equation. We consider also the case in which a quantity other than the number of particle is conserved. The conservative ensembles can be useful in the study of phase transitions and critical phenomena particularly discontinuous phase transitions.     

Green's function method for nonequilibrium systems

The causality principle formulated in the paper is offered as a boundary condition for the Schwinger equation. This approach allows study of, in particular, the dynamics of closed, finite systems. An approximate method for solving the equation is offered. A generalization of the Boltzmann equation is obtained for the presence of particle attenuation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 75–80, April, 1973.The author is very grateful to V. L. Bonch-Bruevich for discussion of the work.     

A nonequilibrium entropy for dynamical systems

It is proposed to define entropy for nonequilibrium ensembles using a method of coarse graining which partitions phase space into sets which typically have zero measure. These are chosen by considering the totality of future possibilities for observation on the system. It is shown that this entropy is necessarily a nondecreasing function of the timet. There is no contradiction with the reversibility of the laws of motion because this method of coarse graining is asymmetric under time reversal. Under suitable conditions (which are stated explicitly) this entropy approaches the equilibrium entropy ast+ and the fine-grained entropy ast–. In particular, the conditions can always be satisfied if the system is aK-system, as in the Sinai billiard models. Some theorems are given which give information about whether it is possible to generate the partition used here for coarse graining from time translates of a finite partition, and at the same time elucidate the connection between our concept of entropy and the entropy invariant of Kolmogorov and Sinai.Research supported in part by NSF grants PHY78-03816 and PHY78-15920.     

Generic two-phase coexistence in nonequilibrium systems

A beautifully simple model introduced a couple of decades ago, Tooms cellular automaton, revealed that non-equilibrium systems may exhibit generic bistability, i.e. two-phase coexistence over a finite area of the (two-dimensional) phase diagram, in violation of the equilibrium Gibbs phase rule. In this paper we analyse two interfacial models, describing more realistic situations, that share with Tooms model a phase diagram with a broad region of phase coexistence. An analysis of the interfacial models yields conditions for generic bistability in terms of physically relevant parameters that may be controlled experimentally.     

Existence of the thermodynamic limit in nonequilibrium systems

The existence of a thermodynamic limit in nonequilibrium stochastic and quantal systems is proven for finite-range interactions and macrovariables which are bounded in the sense of norm. This condition is easily confirmed to be satisfied for specific models, such as the kinetic Ising model and quantal spin systems.Partially financed by Japanese Scientific Research Fund of the Ministry of Education.