Nonequilibrium Steady Research Articles

Time evolution of electron distributions to bimodal steady states for electrons dilutely dispersed in theinert gases Ar, Kr, and Xe with deep Ramsauer Townsend minima in themomentum transfer cross section

The current paper considers the thermalization of an ensemble of electrons under the influence of an external electric field and dilutely dispersed in one of the inert gas moderators, Argon, Krypton or Xenon for which the electron momentum transfer cross sections have deep Ramsauer-Townsend minima. As a consequence, the steady state electron distribution functions are bimodal over a small range of external electric field strengths. The current work is directed towards the time evolution of the electron distribution function determined from the numerical solution of the Fokker-Planck equation. The kinetic theory of electrons dilutely dispersed in a heat bath of atoms at temperature T b has a very long history. The solution of the Fokker-Planck equation can be expressed as a sum of exponentials of the form where λ n are the eigenvalues of the Fokker-Planck operator. Alternatively, a finite difference algorithm is used to solve the time dependent Fokker-Planck equation to give the time dependent electron energy distribution function. We demonstrate the evolution of the initial Maxwellian into a nonequilibrium bimodal distribution which cannot be rationalized with either the Gibbs-Boltzmann entropy or the Tsallis nonextensive entropy. Instead, the time dependent approach of an initial Maxwellian to the bimodal distribution is described in terms of the Kullback-Leibler entropy. We also demonstrate the inapplicability of the Boltzmann entropy nor the Tsallis entropy for a model system with a power law momentum transfer cross section of the form, σ(x) = σ 0/x p , where is the reduced speed. This model with p = 2 is also employed to demonstrate a steady-state Kappa distribution which features prominently in space physics and other fields. For p > 2, we show distribution functions that increase without bound analogous to runaway electrons. The steady nonequilibrium distributions are interpreted as solutions of a Pearson ordinary differential equation.

Factors of the Environmental Components of the Population Quality of Life

The current complex crisis situation in the world presents the scientific community with the task of developing theoretical and methodological provisions and models that are adequate to describe natural systems, while being sufficiently applicable to assess socio-economic processes. The article attempts to analysis of factors of the environmental component of the quality of life of the population. For more than a hundred years, physical laws and analogies have been used to analyze social and economic systems. An attempt to use the laws of nature in the preparation of solutions for the management of social and economic systems is made by the environmental economy. An analysis of the history of the formation and development of the ecological economy was carried out, as a result of which its new direction was revealed, based on a natural science approach and a systemic energy analysis of socio-economic systems. Consideration of the factors of quality of life is carried out from the point of view of the principle of steady non-equilibrium of E.S. Bauer and the natural science foundations of labor, set forth in the works of S.A. Podolinsky. The main hypothesis of the study, the theoretical and methodological foundations of the natural science approach and systemic energy analysis of socio-economic systems related to the study of the relationship between society and the natural environment, with the laws of the functioning of living systems (works of E.S. Bauer, V.I. Vernadsky, A.L. Chizhevsky, etc.). A system of parameters is proposed that allows solving important applied tasks of modeling the environmental component of quality of life in terms of natural science meters without using monetary measures. The selected parameters were modelled on the example of the federal districts of the Russian Federation with the analysis of the identified features and results. The results confirmed the possibility of applying the principles-criteria proposed in the work for the analysis of the development of socio-economic systems in interaction with the environment

Revisiting the Glansdorff–Prigogine Criterion for Stability Within Irreversible Thermodynamics

Glansdorff and Prigogine (1970) proposed a decomposition of the entropy production rate, which today is mostly known for Markov processes as the Hatano-Sasa approach. Their context was irreversible thermodynamics which, while ignoring fluctuations, still allows a somewhat broader treatment than the one based on the Master or Fokker-Planck equation. Glansdorff and Prigogine were the first to introduce a notion of excess entropy production rate $\delta^2$EP and they suggested as sufficient stability criterion for a nonequilibrium macroscopic condition that $\delta^2$EP be positive. We find for nonlinear diffusions that their excess entropy production rate is itself the time-derivative of a local free energy which is the close-to-equilibrium functional governing macroscopic fluctuations. The positivity of the excess $\delta^2$EP, for which we state a simple sufficient condition, is therefore equivalent with the monotonicity in time of that functional in the relaxation to steady nonequilibrium. There also appears a relation with recent extensions of the Clausius heat theorem close-to-equilibrium. The positivity of $\delta^2$EP immediately implies a Clausius (in)equality for the excess heat. A final and related question concerns the operational meaning of fluctuation functionals, nonequilibrium free energies, and how they make their entr\'ee in irreversible thermodynamics.

Monotonic Return to Steady Nonequilibrium

We propose and analyze a new candidate Lyapunov function for relaxation towards general nonequilibrium steady states. The proposed functional is obtained from the large time asymptotics of time-symmetric fluctuations. For driven Markov jump or diffusion processes it measures an excess in dynamical activity rates. We present numerical evidence and we report on a rigorous argument for its monotonic time dependence close to the steady nonequilibrium or in general after a long enough time. This is in contrast with the behavior of approximate Lyapunov functions based on entropy production that when driven far from equilibrium often keep exhibiting temporal oscillations even close to stationarity.

Heat conduction of the hard point chain at zero pressure

Equilibrium and nonequilibrium studies of a hard point chain are performed under thecondition of a vanishing external pressure. If all particles have the same mass, the dynamicsis integrable, but the evolution is highly nontrivial. Numerical simulations in fact revealthat the particle velocities (which are integrals of motion) subdiffuse at equilibrium, whilethey superdiffuse in steady nonequilibrium regimes. This latter behaviour induces ananomalous thermal conductivity similar to that seen in standard ergodic models. Thecomplexity of the dynamics can be traced back to a peculiar property of the hard pointchain which acts as a velocity-dependent filter. Finally, an accurate study of a diatomic(ergodic) chain is performed, which reveals that the thermal conductivity diverges asN2/5 with thenumber N of particles. This analysis confirms the conjecture that one-dimensional systems belong to adifferent universality class when the thermodynamic pressure vanishes.

ERRATUM: "QUANTUM MACROSTATISTICAL THEORY OF NONEQUILIBRIUM STEADY STATES"

We provide a general macrostatistical formulation of nonequilibrium steady states of reservoir driven quantum systems. This formulation is centred on the large scale properties of the locally conserved hydrodynamical observables, and our basic assumptions comprise (a) a chaoticity hypothesis for the nonconserved currents carried by these observables, (b) an extension of Onsager's regression hypothesis to the fluctuations about nonequilibrium states, and (c) a certain mesoscopic local equilibrium hypothesis. On this basis we obtain a picture wherein the fluctuations of the hydrodynamical observables about a nonequilibrium steady state execute a Gaussian Markov process of a generalized Onsager-Machlup type, which is completely determined by the position dependent transport coefficients and the equilibrium entropy function of the system. This picture reveals that the transport coefficients satisfy a generalized form of the Onsager reciprocity relations in the nonequilibrium situation and that the spatial correlations of the hydrodynamical observables are generically of long range. This last result constitutes a model-independent generalization of that obtained for special classical stochastic systems and marks a striking difference between the steady nonequilibrium and equilibrium states, since it is only at critical points that the latter carry long range correlations.

QUANTUM MACROSTATISTICAL THEORY OF NONEQUILIBRIUM STEADY STATES

We provide a general macrostatistical formulation of nonequilibrium steady states of reservoir driven quantum systems. This formulation is centered on the large scale properties of the locally conserved hydrodynamical observables, and our basic physical assumptions comprise (a) a chaoticity hypothesis for the nonconserved currents carried by these observables, (b) an extension of Onsager's regression hypothesis to fluctuations about nonequilibrium states, and (c) a certain mesoscopic local equilibrium hypothesis. On this basis, we obtain a picture wherein the fluctuations of the hydrodynamical variables about a nonequilibrium steady state execute a Gaussian Markov process of a generalized Onsager–Machlup type, which is completely determined by the position dependent transport coefficients and the equilibrium entropy function of the system. This picture reveals that the transport coefficients satisfy a generalized form of the Onsager reciprocity relations in the nonequilibrium situation and that the spatial correlations of the hydrodynamical observables are generically of long range. This last result constitutes a model-independent quantum mechanical generalization of that obtained for special classical stochastic systems and marks a striking difference between the steady nonequilibrium and equilibrium states, since it is only at critical points that the latter carry long range correlations.

Fractal dimension of steady nonequilibrium flows.

The Kaplan-Yorke information dimension of phase-space attractors for two kinds of steady nonequilibrium many-body flows is evaluated. In both cases a set of Newtonian particles is considered which interacts with boundary particles. Time-averaged boundary temperatures are imposed by Nose-Hoover thermostat forces. For both kinds of nonequilibrium systems, it is demonstrated numerically that external isothermal boundaries can drive the otherwise purely Newtonian flow onto a multifractal attractor with a phase-space information dimension significantly less than that of the corresponding equilibrium flow. Thus the Gibbs' entropy of such nonequilibrium flows can diverge.

The nonequilibrium electromotive force. I. Measurements in a continuously stirred tank reactor

Based on a statistical thermodynamic theory, it has been predicted [J. Keizer, J. Chem. Phys. 82, 2751 (1985)] that at nonequilibrium steady states the electromotive force (EMF) of an electrochemical cell will differ from the local equilibrium value given by the Nernst equation. We describe here experiments designed to test this prediction for aqueous solutions of Fe2+ and Fe3+ in sulfate buffer. Using a continuously stirred tank reactor driven by a peristaltic pump, a feed solution containing Fe2+ and Fe3+ was mixed with a second feed solution containing the oxidant sodium peroxydisulfate Na2S2O8. The reaction leads to a steady nonequilibrium mixture, which at acidic pH in sulfate buffer is composed of Fe2+ and the ferric sulfate complexes FeSO+4 and Fe(SO4)−2. The EMF of this half-cell was measured vs a saturated calomel reference electrode as a function of residence time in the reactor. These potentials were compared to the Nernst potential calculated on the basis of the concentration ratio of Fe2+ to total Fe3+ at the steady states. The Nernst potential was reproducibly larger than the measured EMF by values that depended on the concentration ratio of Fe2+/Fe3+ in the feed solution and the residence time. The largest deviations were −1.8 mV, which occurred when the Fe2+/Fe3+ ratio was small and the residence time was about 40 s. We have ruled out streaming potentials, junction potentials, and incomplete mixing as the origin of this effect. We show that the dependence of the nonequilibrium portion of the EMF on feed concentrations and residence time is in good agreement with calculations based on methods that are described in the second paper in this series.