Nonlinear Irreversible Thermodynamics Research Articles

A unified theory for modelling nonequilibrium and equilibrium gas flows

For over 50 years, gas flows have usually been investigated in computational fluid dynamics by using the Navier–Stokes–Fourier framework. Unfortunately, Navier–Stokes–Fourier fails to describe non-equilibrium states. To fill this gap, we give a thermodynamically consistent generalized hydrodynamic theory to develop a unified framework for both equilibrium and nonequilibrium gas flows. The critical step is that we extend the linear Rayleigh–Onsager dissipation to highly nonlinear dissipation to treat nonlinear irreversible thermodynamics. This extension fulfils the positive entropy generation criterion. The solutions of the generalized hydrodynamic theory are compared with experimental and/or particle-based direct simulation Monte Carlo data of the characteristic equilibrium and nonequilibrium gas flows. Good agreement is observed, as expected. The significance of this study is that it provides a unified framework for modelling nonequilibrium and equilibrium gas flows.

Time-Neutrality of Natural Laws Challenged: Time Is Not an Illusion but Ongoing Energy-Driven Information Loss

It is shown that the time of entropy increase, here called action time, is caused by a dynamically understood energy. It drives time by decreasing its presence per state, that is by abandoning order, information, and creating entropy. This mechanism can be derived from basic principles via the Lagrange-Euler formalism, just considering the properties of really experienced, oriented time and thus abandoning the paradigm of time neutrality. It describes nature driven by a dynamically understood principle of least action, which is identified as manifestation of fundamental irreversibility in nature. This readily explains the second law of thermodynamics and also yields the entropy law for non-linear irreversible thermodynamics: maximum entropy production within the restraints of the system. Dynamic energy-driven time, action time, and time asymmetry is generated via the process of erasing information and liberating its energy irreversibly as heat. It is not an illusion but information-based reality. It is the loss of information to the past and different from clock-time, which is just an artificial scale, using information for tracking real time, action time. Energy-driven fundamental irreversibility of nature can better describe experienced reality and opens the way to understand and finally imitate the self-organizing creativity in nature. It also draws far reaching consequences for understanding quantum physics, gravitation and cosmology as well as biology. From the point of view of irreversibility, nature turns out to be more elegant, simpler and rationally understandable. For the first time, it can be explained in a few words what energy and nature basically represent and why it must have been information, which has started the universe.

Nonlinear dissipation and nonequilibrium gas flows.

Rayleigh and Onsager showed that in the regime where the flows are small and the thermodynamic forces vary slowly, the entropy generation rate is linearly related to the flows, and the flows are related to the gradient of the forces. Hence, the Rayleigh-Onsager dissipation is only applicable to linear irreversible thermodynamics. We introduce the extension of Rayleigh-Onsager dissipation to highly nonlinear dissipation to treat nonlinear irreversible thermodynamics. This extension fulfills the positive entropy generation criterion. To demonstrate this nonlinear dissipation, we apply it to obtain the generalized hydrodynamics from the kinetic theory according to Eu theory. Specifically, it provides an alternative evolution for a stress tensor and heat flux. The challenging problems of nonlinear irreversible thermodynamics, as represented by nonequilibrium flows, are investigated. The result implies that this study provides a promising alternative to obtain a unified framework for modeling both equilibrium and nonequilibrium gas flows.

Calcium and temperature effect on structural damage of hot air dried apple slices: Nonlinear irreversible thermodynamic approach and rehydration analysis

Mathematical models traditionally employed in fitting convective drying data do not use to report information about chemical and other physical changes different from the simple decrease in moisture content. In the present study, structural damage undergone by fresh and vacuum impregnated apple slices with different calcium lactate concentrations during convective drying at 30, 40 and 50 °C was analysed by applying equations derived from nonlinear irreversible thermodynamics to experimental data. According to the results obtained, vacuum impregnation with isotonic sucrose solution before drying at 30 °C provided maximum protection to cellular structure by promoting reversible deformations against irreversible breakages. On the contrary, cell walls strengthen with calcium had severe damaged during drying. Regarding air temperature, it was directly related both to the molar energy employed in deforming structures and the drying rate. These results were confirmed by analysing dried samples behaviour during further rehydration.

Heat devices in nonlinear irreversible thermodynamics

We present results obtained by using nonlinear irreversible models for heat devices. In particular, we focus on the global performance characteristics, the maximum efficiency and the efficiency at maximum power regimes for heat engines, and the maximum coefficient of performance (COP) and the COP at maximum cooling power regimes for refrigerators. We analyze the key role played by the interplay between irreversibilities coming from heat leaks and internal dissipations. We also discuss the relationship between these results and those obtained by different models.

Constitutive relation for nonlinear response and universality of efficiency at maximum power for tight-coupling heat engines.

We present a unified perspective on nonequilibrium heat engines by generalizing nonlinear irreversible thermodynamics. For tight-coupling heat engines, a generic constitutive relation for nonlinear response accurate up to the quadratic order is derived from the stalling condition and the symmetry argument. By applying this generic nonlinear constitutive relation to finite-time thermodynamics, we obtain the necessary and sufficient condition for the universality of efficiency at maximum power, which states that a tight-coupling heat engine takes the universal efficiency at maximum power up to the quadratic order if and only if either the engine symmetrically interacts with two heat reservoirs or the elementary thermal energy flowing through the engine matches the characteristic energy of the engine. Hence we solve the following paradox: On the one hand, the quadratic term in the universal efficiency at maximum power for tight-coupling heat engines turned out to be a consequence of symmetry [Esposito, Lindenberg, and Van den Broeck, Phys. Rev. Lett. 102, 130602 (2009); Sheng and Tu, Phys. Rev. E 89, 012129 (2014)]; On the other hand, typical heat engines such as the Curzon-Ahlborn endoreversible heat engine [Curzon and Ahlborn, Am. J. Phys. 43, 22 (1975)] and the Feynman ratchet [Tu, J. Phys. A 41, 312003 (2008)] recover the universal efficiency at maximum power regardless of any symmetry.

Analysis by non-linear irreversible thermodynamics of compositional and structural changes occurred during air drying of vacuum impregnated apple (cv. Granny smith): Calcium and trehalose effects

Apple discs were impregnated with isotonic solutions of sucrose and trehalose with and without calcium addition and after air dried. In the vacuum impregnation experiments, the calcium and the replacement of sucrose by trehalose did not have significant effect on the final volumetric deformation of the samples. During air drying two stages of changes were considered. The first one lasted until the saturation of the intracellular liquid phase, and the second one from the saturation of the intracellular liquid phase until the end of the drying process. Mass transfer has been analysed applying nonlinear irreversible thermodynamics. Water flux, water chemical potential and tissue shrinkage have been taken into account in order to accurately describe the mass transfer phenomena during air drying. A precise definition of chemical potential allowed estimating the partial molar energy needed for breakages and the reversible and irreversible deformations of tissue structure coupled with mass transfer during air drying of apple.

Thermodynamic optimization of energy transfer in (bio)chemical reaction systems

The engineering science literature on energy-transfer processes (heat engines, heat pumps, etc.) for the production of mechanical energy, electricity, cold or heat has produced some remarkable results on maximum power and efficiency optimization. We have wondered in how far these results can be extended to include chemical reaction systems to describe living and possibly future-industrial energy-transfer systems. With elements of non-linear irreversible thermodynamics and chemical kinetics, we have arrived at some interesting results on optimizing the performance of chemical energy transfer. We discuss thermodynamic efficiency, energy-transfer rate, entropy-generation rate, and optimum-performance characteristics of (bio)chemical energy transfer.

On the Onsager Variation Principle and its Generalization for Nonlinear Irreversible Thermodynamics

The Onsager variation principle is examined from the viewpoint of the thermodynamic analogue of the D'Alembert principle in mechanics when the irreversible processes are linear and thus the system is near equilibrium. The thermodynamic D'Alembert principle is shown to be a precursor to the Onsager variation principle. The thermodynamic D'Alembert principle is then generalised to the cases of nonlinear irreversible processes occurring removed from equilibrium and a generalised form of the Onsager variation principle is obtained under some restricting conditions. The restricted variation principle so deduced has an accompanying exact differential form generalising the Clausius entropy differential (equilibrium Gibbs relations) and contains in it the essence of the thermodynamics of irreversible processes in systems where non-linear transport processes occur. An example is given for the nonlinear dissipation function in the variation functional. The evolution equations for fluxes are shown to yield those known in the literature.

Simple model for the instabilities in the aggregation of silica sols in a sol-gel process

A simple kinetic model based on the Prigogine's Brusselator model was used to explain some unstable non-linear oscillations found in the particle size profile of sols in a sol-gel process. These oscillations were explained, in some previous papers, by using the stability criterion from the non-linear irreversible thermodynamics; it is the excess entropy production that characterizes the stability of a system and the occurrence of new structures. In the solgel reaction considered here, one of the steps is auto-catalytic; this fact produces local gradients in the concentration of one of the chemical components, forming a wide variety of new unstable structures. With this model we obtained a relationship for the reaction constants that determines the unstable character of the reaction, and the dependence of the frequency of oscillations on the reactant concentrations. The dependence of the oscillation frequency on water and ethanol concentrations obtained from the experimental data, were well explained by using this model.

On the thermodynamic solution of the Boltzmann equation and nonlinear irreversible thermodynamics

Based on the results of a previous paper on the thermodynamic solution of the Boltzmann equation, some important questions in nonlinear irreversible thermodynamics are reexamined; specifically, the Gibbs relations, the Onsager relations, and the relationship between thermodynamic stability in terms of the entropy balance equation and the dynamical stability of the hydrodynamic equations.

Non-linear irreversible thermodynamics and geochemical systems

Non-linear irreversible thermodynamics and geochemical systems

From a least action principle to mass action law and extended affinity

Basic nonlinear laws that govern nonlinear chemical kinetics and diffusion in a far-from-equilibrium nonstationary regime are derived from an action functional of Hamilton's type. The functional operates with the difference between the kinetic and static free energies F kin and F stat and contains an exponential dissipative term that takes into account thermodynamic irreversibility. Unsteady-state generalization of Guldberg and Waage's kinetic law and Fick's law of diffusion is found which goes over into the classical laws at the steady state when local nonequilibrium effects are ignored. Nonlinear irreversible thermodynamics of chemically reacting systems are investigated. An extended chemical affinity à j is obtained which depends not only on the usual equilibrium quantities T and C but also on nonequilibrium variables such as diffusive fluxes J i and reaction rates r j . It is shown that for a far-from-equilibrium and highly nonstationary regime the thermodynamic force for the j-th chemical reaction, X j ch, is the sum of à j and the time derivative of the so-called “reaction momentum” ∂ F kin/∂ r j , and hence the reaction rate r j depends not only on the current state but also on the past history of the reaction.

Entropy criteria applied to pattern selection in systems with free boundaries

The steady state differential or integral equations which describe patterned dissipative structures, typically to be identified with first order phase transformation morphologies like isothermal pearlites, are invariably degenerate in one or more order parameters (the lamellar spacing in the pearlite case). It is often observed that a different pattern is attained at the steady state for each initial condition (the hysteresis or metastable case). Alternatively, boundary perturbations and internal fluctuations during transition up to, or at the steady state, destroy the path coherence. In this case a statistical ensemble of imperfect patterns often emerges which represents a fluctuating but recognizably patterned and unique average steady state. It is cases like cellular, lamellar pearlite, involving an assembly of individual cell patterns which are regularly perturbed by local fluctuation and growth processes, which concern us here. Such weakly fluctuating nonlinear steady state ensembles can be arranged in a thought experiment so as to evolve as subsystems linking two very large mass-energy reservoirs in isolation. Operating on this discontinuous thermodynamic ideal, Onsager’s principle of maximum path probability for isolated systems, which we interpret as a minimal time correlation function connecting subsystem and baths, identifies the stable steady state at a parametric minimum or maximum (or both) in the dissipation rate. This nonlinear principle is independent of the Principle of Minimum Dissipation which is applicable in the linear regime of irreversible thermodynamics. The statistical argument is equivalent to the weak requirement that the isolated system entropy as a function of time be differentiable to the second order despite the macroscopic pattern fluctuations which occur in the subsystem. This differentiability condition is taken for granted in classical stability theory based on the 2nd Law. The optimal principle as applied to isothermal and forced velocity pearlites (in this case maximal) possesses a Le Chatelier (perturbation) Principle which can be formulated exactlyvia Langer’s conjecture that “each lamella must grow in a direction which is perpendicular to the solidification front”. This is the first example of such an equivalence to be experimentally and theoretically recognized in nonlinear irreversible thermodynamics. A further application to binary solidification cells is reviewed. In this case the optimum in the dissipation is a minimum and the closure between theory and experiment is excellent. Other applications in thermal-hydraulics, biology, and solid state physics are briefy described.

Did nonlinear irreversible thermodynamics revolutionize the classical time conception of physics?

From both physical and epistemological viewpoints, the following theses, which nowadays are often discussed in the literature, are examined: Nonlinear thermodynamics renders it possible to grasp evolutionary physical processes; for thermodynamics it introduces, instead of idealized reversible time, a directed time into physics; thus a science is established that is nearer to reality than classical physics. To analyze these theses, the relation of thermodynamics to dynamical physics is considered. In particular, it is demonstrated that, in classical as well as in modern thermodynamics, irreversibility is introduced via conditions which must be formulated in addition to the dynamical laws. To show the reason for this, the epistemological status of the physical time conception is analyzed, and its character as a physical measurement quantity is established.

Molecular dynamics simulations of the rheological properties of simple fluids

Abstract We review some of the principal results obtained from non-equilibrium molecular dynamics simulations of Couette flow in fluids. The simulations show that even simple fluids exhibit a wide variety of non-Newtonian behaviour (e.g., viscoelasticity, shear thinning and dilatancy, normal stress differences and non-local momentum transport). The asymptotic dispersion relations for each of these effects is consistent with the non-analytic functional forms predicted using “long-time-tail” theories. However in each case, the magnitude of the observed effect is much larger than theoretical predictions. We show that non-linear irreversible thermodynamics successfully relates a number of these non-Newtonian effects observed, very far from equilibrium, outside the regime of local thermodynamic equilibrium.

Molecular dynamic simulations of systems undergoing shear

Non-equilibrium molecular dynamics have been used to simulate, at a molecular level, fluids undergoing planar Couette flow. The results give a microscopic picture of the processes involved in viscoelasticity, shear dilatancy, shear birefringence, normal stress effects and shear thinning behavior. The calculations prove that shear dilatant fluids are not necessarily shear thickening. The results also suggest that the constitutive relations governing non-Newtonian behavior are non-analytic functions of strain rate. The calculations have led directly to the development of non-linear irreversible thermodynamics. This generalization of thermodynamics provides a macroscopic understanding of such processes as shear induced phase changes and the relation of shear dilatancy to shear induced energy changes.

On the extended Gibbs relations and nonlinear irreversible thermodynamics

The consequences of the extended Gibbs relation previously derived from the Boltzmann kinetic theory are further considered and various extensions of equilibrium thermodynamic relations are made into the realm of nonlinear irreversible thermodynamics. Especially, local and global stability theories are presented along with the stability criteria.

New variational-Lagrangian thermodynamics of viscous fluid mixtures with thermomolecular diffusion

A principle of virtual dissipation generalizing d’Alembert’s principle to nonlinear irreversible thermodynamics is applied to viscous fluid mixtures with coupled thermomolecular diffusion. Original dynamical field equations are obtained directly from the variational principle. The use of new fundamental concepts and methods in the thermodynamics of open systems avoids the difficulties inherent in the classical Gibbs approach.The dissipative forces incorporated explicitly in the field equations are expressed by means of a dissipation invariant evaluated in detail in terms of coupled viscous and diffusive properties. Partial pressures and dissipative stresses are given new, unambiguous thermodynamic definitions. Lagrangian type equations with generalized coordinates are also obtained directly from the variational principle. They provide a powerful tool of simplified analysis of complex open systems as well as the foundation of a variety of finite element methods.

Variational thermodynamics of viscous compressible heat-conducting fluids

A new variational principle of virtual dissipation generalizing d’Alembert’s principle to nonlinear irreversible thermodynamics is applied to compressible heat-conducting fluids with Newtonian and non-Newtonian viscosity. The principle is applied in the context of Eulerian formalism where the flow is described with reference to a fixed coordinate system. New concepts of entropy displacement and mass displacement are used as well as a new definition of the chemical potential which avoids the usual ambiguities of the classical thermodynamic approach. The variational principle is used to derive a novel form of field differential equations for the coupled fluid dynamics and convective heat transfer.