Showing papers on "Non-equilibrium thermodynamics published in 1984"

Molecular dynamics with coupling to an external bath.

Abstract: In molecular dynamics (MD) simulations the need often arises to maintain such parameters as temperature or pressure rather than energy and volume, or to impose gradients for studying transport properties in nonequilibrium MD A method is described to realize coupling to an external bath with constant temperature or pressure with adjustable time constants for the coupling The method is easily extendable to other variables and to gradients, and can be applied also to polyatomic molecules involving internal constraints The influence of coupling time constants on dynamical variables is evaluated A leap‐frog algorithm is presented for the general case involving constraints with coupling to both a constant temperature and a constant pressure bath

Nonequilibrium steady states of stochastic lattice gas models of fast ionic conductors

Abstract: We investigate theoretically and via computer simulation the stationary nonequilibrium states of a stochastic lattice gas under the influence of a uniform external fieldE. The effect of the field is to bias jumps in the field direction and thus produce a current carrying steady state. Simulations on a periodic 30 × 30 square lattice with attractive nearest-neighbor interactions suggest a nonequilibrium phase transition from a disordered phase to an ordered one, similar to the para-to-ferromagnetic transition in equilibriumE=0. At low temperatures and largeE the system segregates into two phases with an interface oriented parallel to the field. The critical temperature is larger than the equilibrium Onsager value atE=0 and increases with the field. For repulsive interactions the usual equilibrium phase transition (ordering on sublattices) is suppressed. We report on conductivity, bulk diffusivity, structure function, etc. in the steady state over a wide range of temperature and electric field. We also present rigorous proofs of the Kubo formula for bulk diffusivity and electrical conductivity and show the positivity of the entropy production for a general class of stochastic lattice gases in a uniform electric field.

Nonlinear-response theory for steady planar Couette flow

Abstract: We present a simplified derivation of the Yamada-Kawasaki formula for the nonlinear adiabatic response of the stress tensor to planar Couette flow. This formally exact expression is then used to prove the validity of two nonequilibrium molecular-dynamics algorithms that have been used to study fluids undergoing planar Couette flow, very far from equilibrium.

Transcription of ground-state density-functional theory into a local thermodynamics

Abstract: The concepts of local temperature, local entropy, and local free energy density are introduced within the framework of the ground-state density-functional theory of many-electron systems, and a complete local thermodynamic picture is then developed. A view emerges of the electron cloud, as analogous to a classical inhomogeneous fluid moving under gradients of temperature, pressure, and an effective potential, described by a locally Maxwellian distribution.

Stability criteria and fluctuations around nonequilibrium states

Abstract: A stochastic formulation of the stability of, nonequilibrium states is discussed. An entropy balance equation, including the effect of both the macroscopic evolution and of the fluctuations is derived. In the linear region of thermodynamics Prigogine's minimum entropy production, theorem is extended to include the effect of fluctuations. The latter are shown to reinforce the return of the system to its steady state distribution.

Is equilibrium always an entropy maximum

Abstract: A systematic development is given of the view that in the case of systems with long-range forces and which are therefore nonextensive (in some sense) some thermodynamic results do not hold. Among these is the relationU − TS + pΝ = ΜN and the Gibbs-Duhem equation. If a search for an equilibrium state is made by maximization of the entropy one may obtain misleading results because superadditivity may be violated. The considerations are worked out for a simple gas model, but they are relevant to black hole thermodynamics. Rather general conclusions can be drawn which transcend special systems.

Slow relaxational processes in the melting of linear biopolymers: a theory and its application to nucleic acids.

Abstract: We treat the problem of the mean time of complete separation of complementary chains of a duplex containing N base pairs. A combination of analytical and computer methods is used to obtain the exact solution in the form of a compact expression. This expression is used to analyze the limits of application of the equilibrium theory of helix–coil transition in oligo- and polynucleotides. It also allows the melting behavior of a biopolymer to be predicted when its melting is nonequilibrium. In the case of oligonucleotides for which the equilibrium melting takes place at a high value of the stability constant s, the general expression turns into the equation of Craig, Crothers, and Doty, used by them to determine the rate constant kf of the growth of a helical region from temperature-jump experiments. For the case of fragmented DNA with N ∼ 102, the melting process is shown to be completely nonequilibrium, and as a result, the observed melting temperature should be higher than that for the equilibrium. A simple equation is obtained that makes possible calculation of the real, “kinetic” melting temperature Tk. As N increases, the observed melting temperature should approach the equilibrium value, Tm. This analysis has explained quantitatively the peculiar chain-length dependence of the experimentally observed shift in the DNA melting temperature during fragmentation. A thorough analysis is given of the nonequilibrium effects in the melting process of long DNA molecules (N ≳ 103). The main conclusion is that even in the presence of profound hysteresis phenomena, the melting profile observed on heating may differ only slightly from the equilibrium profile.

Stationary nonequilibrium states by molecular dynamics. II. Newton's law

Abstract: We present molecular-dynamics results for a dense Lennard-Jones fluid near the triple point subjected to the Couette flow. The method is based on the introduction of stochastic boundary conditions to simulate the contact with a moving thermal wall. The method allows the simulation of bulk properties of the system and the study of the local thermodynamical equilibrium. Furthermore, it gives a physical description of momentum and heat transfer near a Couette wall. We found that the shear viscosity depends on shear rate near the triple point (breakdown of Newton's law) while for a point far from the liquid-solid coexistence line there is no appreciable deviation from Newton's law. In the bulk region, where boundary effects are negligible, we found that the local thermodynamical equilibrium holds for all simulated shear rates (up to 1.14\ifmmode\pm\else\textpm\fi{} ${10}^{11}$ ${\mathrm{sec}}^{\ensuremath{-}1}$). Moreover, we do not find any dependence on the number of particles used in the simulation. Last we compare the results for the shear-dependent shear viscosity with theoretical predictions for nonlinear behavior.

Quantum thermodynamics. A new equation of motion for a single constituent of matter

Abstract: A novel nonlinear equation of motion is proposed for quantum systems consisting of a single elementary constituent of matter. It is satisfied by pure states and by a special class of mixed states evolving unitarily. But, in general, it generates a nonunitary evolution of the state operator. It keeps the energy invariant and causes the entropy to increase with time until the system reaches a state of equilibrium or a limit cycle.

Onset of spatial correlations in nonequilibrium systems: A master-equation description

Abstract: The emergence of spatial correlations around a nonequilibrium steady state is studied by means of a stochastic description based on a multivariate master equation The dependence of the strength and range of the correlations on the distance from equilibrium is determined The formalism is applied to chemically reacting systems and to simple fluids submitted to a temperature gradient

Thermodynamics of Mixtures of Fluids

Abstract: Since the first edition of TRUESDELL’s Rational Thermodynamics the thermodynamic theory of mixtures has been improved by the formulation of a more general entropy inequality and by its systematic exploitation through use of Lagrange multipliers.

Numerical solution of the nonlinear boltzmann equation for nonequilibrium gas flow problems

Abstract: This review concerns the numerical solution of the nonlinear Boltzmann equation for a gas flow under conditions far from thermal equilibrium. The rarefied-gas flow problem, which is characterized by a large global parameter, the Knudsen number, is often thought to be the orily non­ equilibrium problem. An appropriate measure of the local departure from equilibrium is the local Knudsen number, which may be defined in terms of the local property gradient. Nonequilibrium conditions characterized by large pro perty gradients do occur in certain regions in continuum-flow problems : a shock wave is a familiar example. Since equilibrium conditions exist in the upstream and downstream regions of the shock wave and since the relations between the upstream and downstream properties are known, the internal shock structure is not needed for the solution of such continuum-flow problems. Another example, which is less familiar, is the Knudsen layer next to an evaporation or a condensation interface. In contrast to the shock wave, the condition of the vapor at the inte rface is far from equilibrium. Neither this nonequilibrium condition nor its relation with the downstream equilibrium condition is known. This Knudsen-layer problem, therefore, cannot be treated by using a continuum approach, even though the flow characteristics in this layer may not be of interest. One of

On the foundations of extended irreversible thermodynamics

Abstract: A theory of macroscopic systems which takes as independent variables the slow (conserved) ones plus the fast dissipative fluxes is carefully analyzed at three levels of description: macroscopic (thermodynamic), microscopic (projection operators) and mesoscopic (fluctuation theory). Such a description is compared with the memory function approach based only on the conserved variables. We find that the first theory is richer and wider than the second one, and some misunderstandings in this connection are clarified and discussed.

Prandtl number effect on benard convection in porous media.

Abstract: A numerical study of buoyance-driven two-dimensional convection in a fluid-saturated horizontal porous layer is reported emphasizing the nonlinear inerital effect on heat transport. The Forchheimer-Brinkman-Darcy-Boussinesq formulation and a single energy equation for the volume-average temperature are used. Closure to the wavenumber selection problem is sought through a criterion based on the Glansdorff and Prigogine theory of nonequilibrium thermodynamics. Good agreement with laboratory data and the analogy with th Rayleigh-Benard problem are corroborative facts which justify smililar non-Darcian formulations and demonstrate the role of the quadratic inertial terms in decreasing the mean convective heat transfer across the layer.

Radiation and the Irreversible Thermodynamics of Climate

Abstract: Attempts to link the theory of irreversible thermodynamics to the study of climate have utilized an entity which has been identified as the entropy production rate. However, this entity does not properly account for irreversibility due to the interaction of the radiation field with matter, that is, changes in the entropy of the radiation field, which cannot in general be properly described by the thermodynamic relations, are not accounted for. Calculations show that the entity used in these attempts deviates substantially from the correct rate of entropy production, both in terms of magnitude and sensitivity.

New Variational-Lagrangian Irreversible Thermodynamics with Application to Viscous Flow, Reaction–Diffusion, and Solid Mechanics

Abstract: Publisher Summary This chapter focuses on new variational-Lagrangian irreversible thermodynamics with application to viscous flow, reaction-diffusion, and solid mechanics. The purpose is to present a comprehensive view of a distinct approach to the thermodynamics of irreversible processes that is based on a principle of virtual dissipation. It represents a generalization of d’Alembert's principle of classical mechanics to irreversible thermodynamics and leads to equations of evolution of thermodynamic systems. They are derived directly either as field equations, or as Lagrangian equations. The variational principle represents essentially a probing of the system in the vicinity of a frozen state of evolution. It is accomplished by applying virtual changes that obey constraints of mass and energy conservation and by evaluating the virtual entropy of an equivalent closed and adiabatic system that represents the virtual entropy produced. In this process, the virtual work of the inertial forces is taken into account. This implies a generalization of d’ Alembert's principle of mechanics to include the thermal energy. The chapter discusses about restructured thermodynamics of open systems and the concept of thermobaric transfer. Concepts related to homogeneous mixtures and reformulation of the Gibbs-Duhem theorem are also elaborated. Dynamics of solids with elastoviscous stresses and heat conduction and thermoelasticity is also described.

A remark on the hydrodynamics of the zero-range processes

Abstract: The nonequilibrium stationary hydrodynamical properties of the symmetric nearest neighbor zero-range processes are studied: local equilibrium and Fourier's law are proven to hold, and the bulk diffusion coefficient and the equal time covariance of the limiting nonequilibrium stationary density fluctuations field are computed. The result fits with those already known and confirms some conjectures derived from a time-dependent macroscopic analysis. The very simple proof is based on a result already published but may be not so well known in this context.

Simple model for the structure and thermodynamics of liquid alloys with strong chemical interactions. II. Chemical order and packing constraints

Abstract: A model presented recently by the authors for the structure and thermodynamics of liquid alloys with strong chemical interactions is applied to Na-Pb and Na-Sn. They show that the thermodynamic 'anomalies' observed in these systems arise from the interplay of ordering effects induced by a preferred interaction between unlike atoms and packing effects. They demonstrate that the structural implications of the model are supported by a diffraction experiment.

Molecular kinetic theory of the glass transition

Abstract: An overview of a new molecular kinetic theory of glass-transition phenomena is presented and experimental comparisons of its prediction for a variety of thermal and stress histories reviewed. The theory, which was developed in accordance with the balance of nonequilibrium statistical entropy, is shown to provide a unified interpretation of some recent models. The volume-relaxation process in amorphous polymers over the glass-transition region is regarded as the result of the collapse of a series of free volumes having different levels of energies of hole formation. An applied stress is shown to contribute to the variation of the entropy. An activation volume is introduced as a new tensorial extensive variable. The theory is applied to the phenomenon of physical aging in polymer glasses and shown to provide good quantitative agreement with the results of a well-known experiment on volume recovery of poly(vinyl acetate). This supports the underlying postulate of a fundamental link between the apparent relaxation time and the mean energy of hole formation, the distribution of relaxation times and the free-volume fractions. In contrast to the prevalent thinking toward free volume theories, an explicit expression between Tg and stress is presented and reveals that Tg does not continue to increase at all pressures but levels off to a semi universal asymptote at very high pressure. The calculated effect of stress rate is found to be in good agreement with dynamic viscoelastic measurements.

Objections to a proposal on the rate of entropy production in systems far from equilibrium

Abstract: Theoretical and experimental counter examples are given to a postulate by Sawada that nonequilibrium systems evolve in time along a path of maximum rate of entropy production

Plasticity and Nonequilibrium Thermodynamics

Abstract: In general mechanical processes in continuous media involve dissipation of heat. The exceptions to the rule are deformations of a purely elastic nature and the flow of ideal fluids.

Homogeneous Periodic Heat Flow via Nonequilibrium Molecular Dynamics

Abstract: Two nonequilibrium methods for simulating homogeneous periodic heat flow are applied to 108 three-dimensional soft spheres in both the fluid and face-centered cubic solid phases. Both nonequilibrium methods use irreversible thermodynamics to express heat conductivity in terms of the work required to generate heat flow. The Evans-Gillan method, derived from Green-Kubo theory, correctly reproduces Ashurst's heat conductivities. An approach based on Gauss' principle of least constraint, in which the heat flow is constrained to a fixed value, fails this test. Heat flow is an inhomogeneous, nonlinear function of particle velocities and coordinates. Thus, Gauss' principle cannot be relied upon for treating inhomogeneous nonlinear nonholonomic constraints.