Showing papers on "Non-equilibrium thermodynamics published in 2003"

Optical diagnostics of atmospheric pressure air plasmas

Abstract: Atmospheric pressure air plasmas are often thought to be in local thermodynamic equilibrium owing to fast interspecies collisional exchange at high pressure. This assumption cannot be relied upon, particularly with respect to optical diagnostics. Velocity gradients in flowing plasmas and/or elevated electron temperatures created by electrical discharges can result in large departures from chemical and thermal equilibrium. This paper reviews diagnostic techniques based on optical emission spectroscopy and cavity ring-down spectroscopy that we have found useful for making temperature and concentration measurements in atmospheric pressure plasmas under conditions ranging from thermal and chemical equilibrium to thermochemical nonequilibrium.

Dissipative particle dynamics: A useful thermostat for equilibrium and nonequilibrium molecular dynamics simulations

Abstract: We discuss dissipative particle dynamics as a thermostat to molecular dynamics, and highlight some of its virtues: (i) universal applicability irrespective of the interatomic potential; (ii) correct and unscreened reproduction of hydrodynamic correlations; (iii) stabilization of the numerical integration of the equations of motion; and (iv) the avoidance of a profile bias in boundary-driven nonequilibrium simulations of shear flow. Numerical results on a repulsive Lennard-Jones fluid illustrate our arguments.

Nonequilibrium thermodynamics

Abstract: Aspects of the modern dynamical systems approach to thermodynamics of stationary states out of equilibrium with attention to the original conceptions which arose at the beginnings of Statistical Mechanics

Stoichiometric network theory for nonequilibrium biochemical systems.

Abstract: We introduce the basic concepts and develop a theory for nonequilibrium steady-state biochemical systems applicable to analyzing large-scale complex isothermal reaction networks. In terms of the stoichiometric matrix, we demonstrate both Kirchhoff's flux law sigma(l)J(l)=0 over a biochemical species, and potential law sigma(l) mu(l)=0 over a reaction loop. They reflect mass and energy conservation, respectively. For each reaction, its steady-state flux J can be decomposed into forward and backward one-way fluxes J = J+ - J-, with chemical potential difference deltamu = RT ln(J-/J+). The product -Jdeltamu gives the isothermal heat dissipation rate, which is necessarily non-negative according to the second law of thermodynamics. The stoichiometric network theory (SNT) embodies all of the relevant fundamental physics. Knowing J and deltamu of a biochemical reaction, a conductance can be computed which directly reflects the level of gene expression for the particular enzyme. For sufficiently small flux a linear relationship between J and deltamu can be established as the linear flux-force relation in irreversible thermodynamics, analogous to Ohm's law in electrical circuits.

Evaporation and instabilities of microscopic capillary bridges.

Abstract: The formation and disappearance of liquid bridges between two surfaces can occur either through equilibrium or nonequilibrium processes. In the first instance, the bridge molecules are in thermodynamic equilibrium with the surrounding vapor medium. In the second, chemical potential gradients result in material transfer; mechanical instabilities, because of van der Waals force jumps on approach or a Rayleigh instability on rapid separation, may trigger irreversible film coalescence or bridge snapping. We have studied the growth and disappearance mechanisms of laterally microscopic liquid bridges of three hydrocarbon liquids in slit-like pores. At rapid slit-opening rates, the bridges rupture by means of a mechanical instability described by the Young–Laplace equation. Noncontinuum but apparently reversible behavior is observed when a bridge is held at nanoscopic surface separations H close to the thermodynamic equilibrium Kelvin length, 2rKcosθ, where rK is the Kelvin radius and θ is the contact angle. During the course of slow evaporation (at H > 2rKcosθ) and subsequent regrowth by capillary condensation (at H < 2rKcosθ), the refractive index of the bridge may vary continuously and reversibly between that of the bulk liquid and vapor. The evaporation process becomes irreversible only at the very final stage of evaporation, when the refractive index of the fluid attains virtually that of the vapor. Measured refractive index profiles and the time-dependence of evaporating neck diameters also seem to differ from predictions based on a continuum picture of bridge evaporation far from the critical point. We discuss these findings in terms of the probable density profiles in evolving liquid bridges.

On the origin and the use of fluctuation relations for the entropy

Abstract: Since about a decade various fluctuation relations for the entropy production have been derived and analyzed. These relations deal with symmetries of the entropy production under time-reversal and have been proposed as a non-perturbative generalization of fluctuation–dissipation relations. I describe a unifying framework for understanding these relations and I present an algorithm to derive them. The fluctuation relations all follow from the main observation that in great generality the pathdependent entropy production is the source-term of time-reversal breaking in the Lagrangian over space-time histories. That is illustrated via a number of examples as well as via a general theoretical argument. I move these relations away from the strict dynamical background in which they originated and take them back to the context of statistical mechanics where entropy is understood in the sense of Boltzmann, as measuring the typicality of a manifest condition. I discuss how a relation between work and free energy is naturally put in that framework and how the transient and steady state fluctuation theorems are simple consequences. The fact that fluctuation symmetries for the entropy production are in general only valid asymptotically for large times, makes them mostly inaccessible for experimental verification, in contrast with a recent claim that they would usefully quantify second law violations. Part of the interest in the resulting fluctuation symmetries is that they are so universally valid, a rare occasion in nonequilibrium statistical mechanics. However they do not provide a systematic perturbation expansion for response functions. For that one needs to go back to the full Lagrangian and also consider the nonequilibrium modifications to its time-symmetric part.

Quantification of order in the Lennard-Jones system

Abstract: We conduct a numerical investigation of structural order in the shifted-force Lennard-Jones system by calculating metrics of translational and bond-orientational order along various paths in the phase diagram covering equilibrium solid, liquid, and vapor states. A series of nonequilibrium configurations generated through isochoric quenches, isothermal compressions, and energy minimizations are also considered. Simulation results are analyzed using an ordering map representation [Torquato et al., Phys. Rev. Lett. 84, 2064 (2000); Truskett et al., Phys. Rev. E 62, 993 (2000)] that assigns both equilibrium and nonequilibrium states coordinates in an order metric plane. Our results show that bond-orientational order and translational order are not independent for simple spherically symmetric systems at equilibrium. We also demonstrate quantitatively that the Lennard-Jones and hard sphere systems sample the same configuration space at supercritical densities. Finally, we relate the structural order found in fast-quenched and minimum-energy configurations (inherent structures).

Thermodynamics of alloys and phase equilibria in the copper-iron system

Abstract: Together with previous values at 1873 K, new measurements of the enthalpies of formation of liquid Cu-Fe alloys, carried out by high-temperature calorimetry at 1673 K, have revealed a temperature dependence of ΔH, corresponding to a negative excess heat capacity of mixing Our calorimetric results were combined with critically selected values of the enthalpies of alloying and activities of components in liquid and solid solutions, as well as parameters of stable and metastable phase transitions, to perform a thermodynamic evaluation of the system The latter was carried out in the spirit of the CALPHAD approach, using Thermo-Calc software The thermodynamic model generates a self-consistent description of all thermodynamic properties and phase equilibria, including metastable solidification, in close agreement with reliable experimental data In particular, a very satisfactory representation of stable (L+δ)/γ, (L + γ)/e, γ/(e + α) and metastable (L1/L2), (L1 + L2)/e phase boundaries has been achieved The occurrence of a monotectic reaction L2 ↔ L1 + δ is suggested in the region of the metastable precipitation of δ-phase A comprehensive thermodynamic model of the Cu-Fe system is used to explain the widening of the concentration limits of formation of supersaturated bcc and fcc solutions prepared by highly nonequilibrium methods of synthesis

Depletion Forces in Nonequilibrium

Abstract: The concept of effective depletion forces between two fixed big colloidal particles in a bath of small particles is generalized to a nonequilibrium situation where the bath of small Brownian particles is flowing around the big particles with a prescribed velocity. In striking contrast to the equilibrium case, the nonequilibrium forces violate Newton's third law; they are nonconservative and strongly anisotropic, featuring both strong attractive and repulsive domains.

Equilibrium free energies from path sampling of nonequilibrium trajectories

Abstract: Jarzynski’s relation between equilibrium free energy and nonequilibrium work is rewritten as an average of work with respect to a work weighted ensemble. The present form is more appropriate for computer application of Jarzynski’s relation where the dissipative work is frequently much greater than kBT. Monte Carlo sampling of very short nonequilibrium trajectories yields good estimates of the equilibrium free energy change. The procedure can be thought of as a generalization of thermodynamic integration in ordinary free energy calculations. Very short trajectories can be used to compute the free energy difference. In the infinitely short trajectory limit, we recover the thermodynamic integration scheme. We also show that free energy estimate can be obtained from moments of the work distribution. The last result is most useful for experimental measurements of the free energy.

The radiative response of solar loop plasma subject to transient heating

Abstract: In Bradshaw & Mason (2003) we carried out a hydrodynamic simulation of a cooling solar loop and investigated the nonequilibrium response of the population of C VII ions to the changing conditions in the plasma. We also compared equilibrium and nonequilibrium calculations of the total plasma emissivity. In this paper we present two simulations of a solar loop subject to a transient heating process delivering energy on the nanoflare scale at its apex. One simulation treats the ion populations and the energy radiated from the loop plasma entirely as though the system were in equilibrium and the other simulation performs a full nonequilibrium treatment by coupling the time-dependent ion populations to the hydrodynamic equations through the radiative energy loss. Our radiative model accounts for the 15 most abundant elements of the solar atmosphere including C, O, Ne, Mg, Si and Fe. We find some pronounced dierences between the populations of certain transition region ions and the corresponding plasma emissivity curves in the equilibrium and nonequilibrium simulations. Though the apex heating event is relatively weak in comparison to energy released on the microflare and flare scales, nonetheless a significant amount of energy reaches the loop footpoint region to heat the plasma there and we find a nonequilibrium spike in emissivity. However, more surprisingly we find considerable dierences between some of the coronal ions in the equilibrium and nonequilibrium simulations, with important consequences for the plasma emissivity curves. In particular, we find that the total plasma emissivity calculated assuming equilibrium conditions is up to a factor of 5 lower than the nonequilibrium emissivity and this is due almost entirely to the response of the coronal Fe ions. Finally, we suggest possible observational signatures of nonequilibrium ionisation and ways in which one might identify it. This is important because an invalid assumption of equilibrium ion populations may well lead one to incorrect conclusions about the properties of the plasma in both a broad-band and narrow-band/emission line based analysis.

Extending the definition of entropy to nonequilibrium steady states.

Abstract: We study the nonequilibrium statistical mechanics of a finite classical system subjected to nongradient forces ξ and maintained at fixed kinetic energy (Hoover–Evans isokinetic thermostat). We assume that the microscopic dynamics is sufficiently chaotic (Gallavotti–Cohen chaotic hypothesis) and that there is a natural nonequilibrium steady-state ρξ. When ξ is replaced by ξ + δξ, one can compute the change δρ of ρξ (linear response) and define an entropy change δS based on energy considerations. When ξ is varied around a loop, the total change of S need not vanish: Outside of equilibrium the entropy has curvature. However, at equilibrium (i.e., if ξ is a gradient) we show that the curvature is zero, and that the entropy S(ξ + δξ) near equilibrium is well defined to second order in δξ.

Mass– and volume–specific views on thermodynamics for open systems

Abstract: A general framework for the thermodynamics of open systems is presented. The theory is fundamentally based on the generalized balance of mass, which is enhanced by additional surface–flux and volume–source terms. The presentation highlights the influence of the enhanced mass balance on the remaining balance equations. To clarify the impact of the variable reference density, we introduce the notions of volume–specific and mass–specific formats. Particular attention is drawn to the fact that the mass–specific balance equations are free from explicit open–system contributions. They resemble the classical balance equations and can thus be evaluated in complete analogy to the closed–system case. Restrictions for the constitutive equations follow from the second law of thermodynamics, as illustrated for the particular model problem of thermo–hyperelasticity.

Weakly nonlocal irreversible thermodynamics

Abstract: Weakly nonlocal thermodynamic theories are critically revisited. A relocalized, irreversible thermodynamic theory of nonlocal phenomena is given, based on a modified form of the entropy current and new kind of internal variables, the so called current multipliers. The treatment is restricted to deal with nonlocality connected to dynamic thermodynamic variables. Several classical equations are derived, including Guyer-Krumhansl, Ginzburg-Landau and Cahn-Hilliard type equations.

Universality of anomalous one-dimensional heat conductivity.

Abstract: In one and two dimensions, transport coefficients may diverge in the thermodynamic limit due to long-time correlation of the corresponding currents. The effective asymptotic behavior is addressed with reference to the problem of heat transport in one-dimensional crystals, modeled by chains of classical nonlinear oscillators. Extensive accurate equilibrium and nonequilibrium numerical simulations confirm that the finite-size thermal conductivity diverges with system size L as k}L a . However, the exponent a deviates systematically from the theoretical prediction a51/3 proposed in a recent paper @O. Narayan and S. Ramaswamy, Phys. Rev. Lett. 89, 200601 ~2002!#.

Mesoscopic Nonequilibrium Thermodynamics Gives the Same Thermodynamic Basis to Butler-Volmer and Nernst Equations

Abstract: Mesoscopic nonequilibrium thermodynamics is used to derive the Butler-Volmer equation, or the stationary state nonlinear relation between the electric current density and the overpotential of an electrode surface. The equation is derived from a linear flux-force relationship at the mesoscopic level for the oxidation of a reactant to its charged components. The surface was defined with excess variables (a Gibbs surface). The ButlerVolmer equation was derived using the assumption of local electrochemical equilibrium in the surface on the mesoscopic level. The result was valid for an isothermal electrode with reaction-controlled charge transfer and with equilibrium for the reactant between the adjacent bulk phase and the surface. The formulation that is used for the mesoscopic level is consistent with nonequilibrium thermodynamics for surfaces and, thus, with the second law of thermodynamics. The Nernst equation is recovered in the reversible limit. The reversible/ dissipative nature of the charge-transfer process is discussed on this basis.

Thermodynamics of Self-Gravitating Systems

Abstract: This work assembles some basic theoretical elements on thermal equilibrium, stability conditions, and fluctuation theory in self-gravitating systems illustrated with a few examples. Thermodynamics deals with states that have settled down after sufficient time has gone by. Time dependent phenomena are beyond the scope of this paper. While thermodynamics is firmly rooted in statistical physics, equilibrium configurations, stability criteria and the destabilizing effect of fluctuations are all expressed in terms of thermodynamic functions. The work is not a review paper but a pedagogical introduction which may interest theoreticians in astronomy and astrophysicists. It contains sufficient mathematical details for the reader to redo all calculations. References are only to seminal works or readable reviews. Delicate mathematical problems are mentioned but are not discussed in detail.

Interfacial nonequilibrium and Bénard-Marangoni instability of a liquid-vapor system.

Abstract: We study B\'enard-Marangoni instability in a system formed by a horizontal liquid layer and its overlying vapor. The liquid is lying on a hot rigid plate and the vapor is bounded by a cold parallel plate. A pump maintains a reduced pressure in the vapor layer and evacuates the vapor. This investigation is undertaken within the classical quasisteady approximation for both the vapor and the liquid phases. The two layers are separated by a deformable interface. Temporarily frozen temperature and velocity distributions are employed at each instant for the stability analysis, limited to infinitesimal disturbances (linear regime). We use irreversible thermodynamics to model the phase change under interfacial nonequilibrium. Within this description, the interface appears as a barrier for transport of both heat and mass. Hence, in contrast with previous studies, we consider the possibility of a temperature jump across the interface, as recently measured experimentally. The stability analysis shows that the interfacial resistances to heat and mass transfer have a destabilizing influence compared to an interface that is in thermodynamic equilibrium. The role of the fluctuations in the vapor phase on the onset of instability is discussed. The conditions to reduce the system to a one phase model are also established. Finally, the influence of the evaporation parameters and of the presence of an inert gas on the marginal stability curves is discussed.

Extended thermodynamics - consistent in order of magnitude

Abstract: It was always known that ordinary thermodynamics requires fairly smooth and slowly varying fields. Extended thermodynamics on the other hand is needed for rapidly changing fields with steep gradients. This notion is made explicit in the present paper by assigning orders of magnitude in steepness to the moments which are the field variables of extended thermodynamics. Once a process is deemed to be steep of O(n), the number of field variables may be read off from a table and the field equations are closed, by omission of all higher order terms. The procedure is demonstrated for stationary one-dimensional heat conduction and for heat conduction and one-dimensional motion. An instructive synthetical case of a “one-dimensional gas” is also treated and it is shown in this case how the hyperbolic equations of extended thermodynamics may be regularized – or parabolized – in a rational manner. The theory of O(n) is fully compatible with the entropy principle of that order, but no entropy postulate is needed here, at least not for closure. The theory can be shown to be compatible with an exponential phase density.

The nonequilibrium van der Waals square gradient model. (II). Local equilibrium of the Gibbs surface

Abstract: In a first paper we extended the van der Waals square gradient model for the equilibrium liquid–vapor interface to nonequilibrium systems, in which both the density and the temperature depend on position and time. In this paper, we defined and calculated the excess densities for an arbitrary choice of the dividing surface in such nonequilibrium systems. Comparing with the thermodynamic relations given by Gibbs we were then able to define a unique temperature and chemical potential of the surface. From numerical results for stationary state evaporation and condensation, we were then able to verify that the “Gibbs surface” is autonomous, i.e., in local equilibrium. Even for temperature gradients in the vapor of a million degrees per cm and evaporation and condensation fluxes up to 2 m / s , we were able to verify this property and to define a unique surface temperature. This autonomous nature of the Gibbs surface is remarkable in view of the non-autonomous nature of the continuous description in the van der Waals model. Results are presented for both the equimolar surface and the surface of tension. A discussion is given of how to transform the thermodynamic densities for the surface from one choice of the dividing surface to the other in the case that there is heat and mass flow through the surface.

Mean-field and anomalous behavior on a small-world network.

Abstract: We consider various equilibrium statistical mechanics models with combined short- and long-range interactions and identify the crossover to mean-field behavior, finding anomalous scaling in the width of the mean-field region, as well as in the mean-field amplitudes. We then show that this model enables us, in many cases, to determine the universal critical properties of systems on a small-world network. Finally, we consider nonequilibrium processes.

The nonequilibrium van der Waals square gradient model. (I). The model and its numerical solution

Abstract: The van der Waals square gradient model has played an important role in the description of the properties of an equilibrium interface between a vapor and a liquid. We extend the model to describe nonequilibrium states with temperature gradients, pressure differences and the resulting evaporation or condensation fluxes. In the equilibrium model van der Waals introduced a square gradient term in the free energy density. This term describes the deviation from local equilibrium in the interfacial region. In this first paper we propose explicit expressions for all the thermodynamic densities needed in the nonequilibrium description. After deriving the entropy production rate we give the linear force–flux relation. It is found that the thermal resistance also contains a square gradient contribution. A numerical procedure to solve the resulting equations in a stationary state was developed and is discussed. A first discussion is given of the properties of the resulting numerical solutions. We discuss in particular how evaporation and condensation fluxes result as a consequence of changing the pressure away from the coexistence pressure and by thermostating the temperatures at the ends of the box in the liquid and the vapor phases away from the equilibrium value. The influence of the size of the square gradient contribution to the thermal resistance on the temperature profiles is assessed.

Homogeneous nucleation in inhomogeneous media. II. Nucleation in a shear flow

Abstract: We investigate the influence of a shear flow on the process of nucleation. Mesoscopic nonequilibrium thermodynamics is used to derive the Fokker–Planck equation governing the evolution of the cluster size distribution in a metastable phase subjected to a stationary flow. The presence of the flow manifests itself in the expression for the effective diffusion coefficient of a cluster and introduces modifications in the nucleation rate. The implications of these results in condensation and polymer crystallization are discussed.

Vertical free convective boundary-layer flow in a porous medium using a thermal nonequilibrium model: Elliptical effects

Abstract: In this paper we study the effect of adopting a two-temperature model of microscopic heat transfer on the classical Cheng & Minkowycz [1] vertical free convection boundary-layer flow in a porous medium. Such a model, which allows the solid and fluid phases not to be in local thermal equilibrium, is found to modify substantially the behaviour of the flow relatively close to the leading edge. A companion paper deals with the (parabolic) boundary-layer theory, but the present work investigates in detail how elliptical effects are manifested. This is undertaken by solving the full equations of motion, rather than the boundary-layer approximation. In general, it is found that at any point in the flow, the temperature of the solid phase is higher than that of the fluid phase, and therefore that the thermal field of the solid phase is of greater extent than that of the fluid phase. The microscopic inter-phase heat transfer is characterised by the coefficient, H, and it is shown that these thermal non-equilibrium effects are strongest when H is small.

Information Theoretic Approach to Fluctuations and Electron Flows between Molecular Fragments

Abstract: The elements of the information theoretic approach to instantaneous electron distributions between molecular subsystems are developed by following the thermodynamic theory of fluctuations and irreversible processes. The distribution function and information theoretic basis of the stockholder partitioning, defining the equilibrium distributions of electrons among subsystems, are briefly summarized. The nonequilibrium (instantaneous) local entropy deficiency and the state parameters and their associated intensive conjugates in the entropy deficiency representation are introduced using the promolecule-referenced local measures of the information distance (entropy deficiency) of Kullback and Leibler between the instantaneous subsystem electron densities, conserving the overall molecular density and the free or Hirshfeld subsystem electron densities, respectively. Within a local description, the Gaussian distribution function of Einstein's theory is introduced, predicting a local dispersion of the subsystem de...

Notes on the Third Law of Thermodynamics.I

Abstract: We analyse some aspects of the third law of thermodynamics. We first review both the entropic version (N) and the unattainability version (U) and the relation occurring between them. Then, we heuristically interpret (N) as a continuity boundary condition for thermodynamics at the boundary T = 0 of the thermodynamic domain. On a rigorous mathematical footing, we discuss the third law both in Caratheodory's approach and in Gibbs' one. Caratheodory's approach is fundamental in order to understand the nature of the surface T = 0. In fact, in this approach, under suitable mathematical conditions, T = 0 appears as a leaf of the foliation of the thermodynamic manifold associated with the non-singular integrable Pfaffian form δQrev. Being a leaf, it cannot intersect any other leaf S = const of the foliation. We show that (N) is equivalent to the requirement that T = 0 is a leaf. In Gibbs' approach, the peculiar nature of T = 0 appears to be less evident because the existence of the entropy is a postulate; nevertheless, it is still possible to conclude that the lowest value of the entropy S has to be attained at the boundary of the convex set where S is defined.

Nonequilibrium thermodynamics and Fisher information: sound wave propagation in a dilute gas.

Abstract: As recently shown, a constrained Fisher-information extremizing (CFIE) process is able to deal with both equilibrium and nonequilibrium thermodynamic processes, thus being able to reproduce results deduced by a recourse to Boltzmann's transport equation (BTE). Here, we discuss the propagation of sound waves in a dilute gas and compare the ensuing CFIE solutions with those obtained by a recourse to Grad's approach to the BTE. The final molecular distribution function arrived at is the same following two alternative routes, either (i) the BTE via the Grad approach or (ii) the constrained Fisher treatment that does not require the use of the BTE. The way the necessary a priori information is used in these two instances, is however, quite different.

Entropy production in nonequilibrium thermodynamics: a review

Abstract: Entropy might be a not well defined concept if the system can undergo transformations involving stationary nonequilibria. It might be analogous to the heat content (once called ``caloric'') in transformations that are not isochoric (i.e. which involve mechanical work): it could be just a quantity that can be transferred or created, like heat in equilibrium. The text first reviews the philosophy behind a recently proposed definition of entropy production in nonequilibrium stationary systems. A detailed technical attempt at defining the entropy of a stationary states via their variational properties follows: the unsatisfactory aspects of the results add arguments in favor of the nonexistence of a function of state to be identified with entropy; at the same time new aspects and properties of the phase space contraction emerge.