Theory Of Irreversible Thermodynamics Research Articles

Onsager’s reciprocal relationship applied to multiphysics poromechanics

Onsager’s theory of linear irreversible thermodynamics has been successfully applied to explain findings from experiments. However, its application to multiphysics processes in deformable porous media is a non-trivial undertaking. This contribution presents an extension of Onsager’s theorem to include the flux of the matter of weakly coupled two-phase porous systems. It also relates Onsager to Ziegler’s nonlinear approach including the classical acoustic tensor criterion for localisation phenomena in such nonlinear media. The results are illustrated by Terzaghi consolidation problem using the well established modified Cam-Clay plasticity model. We show that a generalised dissipative stress can act as an appropriate thermodynamic force quantity rendering the non-associated yield envelope into Onsager’s associated form ensuring the thermodynamic condition of no-work free plastic deformation. We present in this contribution an attempt of using the theory of thermodynamics of internal state variables to develop a generic poromechanics approach that relaxes isothermal constraints for weakly coupled problems. This approach lends itself to a promising future extension of a dynamic Onsager diffusional operator for conditions where the multiphysics processes are strongly coupled in the porous system and emergent phenomena may occur.

Modeling and optimization of salt and boron removal in reverse osmosis system

Seawater reverse osmosis (SWRO) is a mature technology that has significantly evolved over the past few decades. However, boron removal remains a serious challenge. A new RO transport model was developed by combining the irreversible thermodynamic theory and solution-diffusion theory and considering the solute concentration polarization phenomenon. The developed RO model supplemented by the use of variable solution properties and transport parameters was validated with existing data and, it was then applied to identify the main operation parameters and assess their effect on SWRO performance, with the aim of minimizing specific energy consumption and satisfying water quality requirements. The results showed that the solution-diffusion approach, cannot capture the interaction between transported boron and water species. For high pH, applied feed pressure, and flow rate, the convective transport of boron through the seawater membrane is remarkable and its contribution to the overall boron flux can reach over 20 %. The feed operating conditions have significantly influenced the quality of the water production and the amount of energy used. The results showed that the optimal SEC increased by approximately 40 %, and the recovery ratio decreased by 11.6 % as the feed flow rate increased from 0.002 to 0.005 m3/s.

Spin diffusion in spin glasses requires two magnetic variables, M⃗ and m⃗

Experiment has established that spin-glasses can support a steady-state spin current $\vec{j}_{i}$. However, the accepted theory of spin glass dynamics permits oscillations but no steady-state spin current. Onsager's irreversible thermodynamics implies that the spin current is proportional to the gradient of a magnetization. We argue, however, that the magnon distribution function associated with the local equilibrium magnetization $\vec{M}$ cannot diffuse because it represents $10^{23}$ variables. We therefore invoke the non-equilibrium magnetization $\vec{m}$, which in spintronics is called the {\it spin accumulation}. Applying the theory of irreversible thermodynamics we indeed find that it predicts spin diffusion, and we consider other experimental consequences of the theory, including a wavelength-dependent coupling between the reactive and the diffusive degrees of freedom.

How Flexible Is the Concept of Local Thermodynamic Equilibrium?

It has been demonstrated by using generalized phenomenological irreversible thermodynamic theory (GPITT) that by replacing the conventional composition variables {xk} by the quantum level composition variables {x˜k,j} corresponding to the nonequilibrium population of the quantum states, the resultant description remains well within the local thermodynamic equilibrium (LTE) domain. The next attempt is to replace the quantum level composition variables by their respective macroscopic manifestations as variables. For example, these manifestations are, say, the observance of fluorescence and phosphorescence, existence of physical fluxes, and ability to register various spectra (microwave, IR, UV-VIS, ESR, NMR, etc.). This exercise results in a framework that resembles with the thermodynamics with internal variables (TIV), which too is obtained as a framework within the LTE domain. This TIV-type framework is easily transformed to an extended irreversible thermodynamics (EIT) type framework, which uses physical fluxes as additional variables. The GPITT in EIT version is also obtained well within the LTE domain. Thus, GPITT becomes a complete version of classical irreversible thermodynamics (CIT). It is demonstrated that LTE is much more flexible than what CIT impresses upon. This conclusion is based on the realization that the spatial uniformity for each tiny pocket (cell) of a spatially non-uniform system remains intact while developing GPITT and obviously in its other versions.

Riemann solvers for phase transition in a compressible sharp-interface method

In this paper, we consider Riemann solvers with phase transition effects based on the Euler–Fourier equation system. One exact and two approximate solutions of the two-phase Riemann problem are obtained by modelling the phase transition process via the theory of classical irreversible thermodynamics. Closure is obtained by appropriate Onsager coefficients for evaporation and condensation. We use the proposed Riemann solvers in a sharp-interface level-set ghost fluid method to couple the individual phases with each other. The proposed sharp-interface method is validated against molecular dynamics data of evaporating Lennard–Jones truncated and shifted fluid. We further study the effects of phase transition on a shock-drop interaction with the novel approximate Riemann solvers.

Non-Equilibrium Thermodynamic Foundations of the Origin of Life

There is little doubt that life’s origin followed from the known physical and chemical laws of Nature. The most general scientific framework incorporating the laws of Nature and applicable to most known processes to good approximation, is that of thermodynamics and its extensions to treat out-of-equilibrium phenomena. The event of the origin of life should therefore also be amenable to such an analysis. In this review paper, I describe the non-equilibrium thermodynamic foundations of the origin of life for the non-expert from the perspective of the “Thermodynamic Dissipation Theory for the Origin of Life” which is founded on Classical Irreversible Thermodynamic theory developed by Lars Onsager, Ilya Prigogine, and coworkers. A Glossary of Thermodynamic Terms can be found at the end of the article to aid the reader.

A Photon Force and Flow for Dissipative Structuring: Application to Pigments, Plants and Ecosystems.

Through a modern derivation of Planck’s formula for the entropy of an arbitrary beam of photons, we derive a general expression for entropy production due to the irreversible process of the absorption of an arbitrary incident photon spectrum in material and its dissipation into an infrared-shifted grey-body emitted spectrum, with the rest being reflected or transmitted. Employing the framework of Classical Irreversible Thermodynamic theory, we define the generalized thermodynamic flow as the flow of photons from the incident beam into the material and the generalized thermodynamic force is, then, the entropy production divided by the photon flow, which is the entropy production per unit photon at a given wavelength. We compare the entropy production of different inorganic and organic materials (water, desert, leaves and forests) under sunlight and show that organic materials are the greater entropy-producing materials. Intriguingly, plant and phytoplankton pigments (including chlorophyll) reach peak absorption exactly where entropy production through photon dissipation is maximal for our solar spectrum nm, while photosynthetic efficiency is maximal between 600 and 700 nm. These results suggest that the evolution of pigments, plants and ecosystems has been towards optimizing entropy production, rather than photosynthesis. We propose using the wavelength dependence of global entropy production as a biosignature for discovering life on planets of other stars.

Entropic Effects of Interacting Particles Diffusing on Spherical Surfaces

We present a molecular dynamics and theoretical study on the diffusion of interacting particles embedded on the surface of a sphere. By proposing five different interaction potentials among particles, we perform molecular dynamics simulations and calculate the mean square displacement (MSD) of tracer particles under a crowded regime of high surface density. Results for all the potentials show four different behaviors passing from ballistic and transitory at very short times, to sub-diffusive and saturation behaviors at intermediary and long times. Making use of irreversible thermodynamics theory, we also model the last two stages showing that the crowding induces a sub-diffusion process similar to that caused by particles trapped in cages, and that the saturation of the MSD is due to the existence of an entropic potential that limits the number of accessible states to the particles. By discussing the convenience of projecting the motions of the particles over a plane of observation, consistent with experimental capabilities, we compare the predictions of our theoretical model with the simulations showing that these stages are remarkably well described in qualitative and quantitative terms.

The Dissipative Photochemical Origin of Life: UVC Abiogenesis of Adenine.

The non-equilibrium thermodynamics and the photochemical reaction mechanisms are described which may have been involved in the dissipative structuring, proliferation and complexation of the fundamental molecules of life from simpler and more common precursors under the UVC photon flux prevalent at the Earth’s surface at the origin of life. Dissipative structuring of the fundamental molecules is evidenced by their strong and broad wavelength absorption bands in the UVC and rapid radiationless deexcitation. Proliferation arises from the auto- and cross-catalytic nature of the intermediate products. Inherent non-linearity gives rise to numerous stationary states permitting the system to evolve, on amplification of a fluctuation, towards concentration profiles providing generally greater photon dissipation through a thermodynamic selection of dissipative efficacy. An example is given of photochemical dissipative abiogenesis of adenine from the precursor HCN in water solvent within a fatty acid vesicle floating on a hot ocean surface and driven far from equilibrium by the incident UVC light. The kinetic equations for the photochemical reactions with diffusion are resolved under different environmental conditions and the results analyzed within the framework of non-linear Classical Irreversible Thermodynamic theory.

Comparative performance analysis of a Brownian Carnot cycle from the perspective of a stochastic model against the Linear Irreversible Thermodynamics theory

In this paper we present a Brownian Carnot cycle, which has already been studied by Schmield et al. (2007) as well as by Izumida and Okuda (2010); but now considering two different working regimes, namely the Maximum Ecological Function (MEC) and the Maximum Efficient Power (MEP). For the MEC and MEP working regimes, the thermodynamic properties of the cycle are obtained, in particular, it is showed that the maximum efficiency now depends on two parameters α and β, instead of only one parameter obtained previously by Schmiled et al. in the maximum power regime. It is worthwhile to notice that for characteristic values of α and β the original results obtained by Schmield are recovered.From the previous observations, the authors consider that the results obtained represent a more general case that includes other working regimes.

Thermodynamic Consistency and Thermomechanical Dynamics (TMD) for Nonequilibrium Irreversible Mechanism of Heat Engines

The irreversible mechanism of heat engines is studied in terms of thermodynamic consistency and thermomechanical dynamics (TMD) which is proposed for a method to study nonequilibrium irreversible thermodynamic systems. As an example, a water drinking bird (DB) known as one of the heat engines is specifically examined. The DB system suffices a rigorous experimental device for the theory of nonequilibrium irreversible thermodynamics. The DB nonlinear equation of motion proves explicitly that nonlinear differential equations with time-dependent coefficients must be classified as independent equations different from those of constant coefficients. The solutions of nonlinear differential equations with time-dependent coefficients can express emergent phenomena: nonequilibrium irreversible states. The couplings among mechanics, thermodynamics and time-evolution to nonequilibrium irreversible state are defined when the internal energy, thermodynamic work, temperature and entropy are integrated as a spontaneous thermodynamic process in the DB system. The physical meanings of the time-dependent entropy, T(t)dS(t), , internal energy, dƐ(t), and thermodynamic work, dW(t), are defined by the progress of time-dependent Gibbs relation to thermodynamic equilibrium. The thermomechanical dynamics (TMD) approach constitutes a method for the nonequilibrium irreversible thermodynamics and transport processes.

Anisotropic energy-based progressive damage model for laminated geomaterials

Laminated geomaterial widely exists in rock engineering construction. Inherent anisotropy of laminated geomaterial make its mechanical properties and mathematical constitutive model complicated. This study is devoted to developing an energy-based damage model for characterizing both the inherent anisotropy and the stress-induced anisotropy of laminated geomaterials. The fabric tensor is adopted to describe the inherent anisotropy. Then, the free energy potential is defined in combination with the fabric tensor. The general stress-strain relationship and anisotropic stiffness matrix are derived based on the irreversible thermodynamics theory. To reflect the anisotropy of damage during the application of force, a fourth-order damage tensor is defined. This damage tensor is dependent on two scalar damage factors, which depict the degeneration of stiffness along the normal direction of the bedding plane and in the isotropic plane, respectively. Equivalent energy release rates corresponding to these two damage factors are constructed in consideration of the effects of anisotropy. Taking a statistical approach, anisotropic damage evolution rules that distinguish the different mechanical responses of laminated geomaterials under compression and tension are proposed. Moreover, the calibration procedure for the unknown parameters in the model is described in detail, and the predictions from the proposed theoretical model are compared with those from existing models to verify the rationality of the present model. Triaxial compression and tensile tests are also adopted to facilitate a comparison with the results of numerical simulations, illustrating that the new constitutive model can capture the anisotropic mechanical deformation and the anisotropic damage evolution of a laminated geomaterial.

On extended thermodynamics: From classical to the relativistic regime

The recent monumental detection of gravitational waves by LIGO, the subsequent detection by the LIGO/VIRGO observatories of a binary neutron star merger seen in the gravitational wave signal [Formula: see text], the first photo of the event horizon of the supermassive black hole at the center of Andromeda galaxy released by the EHT telescope and the ongoing experiments on Relativistic Heavy Ion Collisions at the BNL and at the CERN, demonstrate that we are witnessing the second golden era of observational relativistic gravity. These new observational breakthroughs, although in the long run would influence our views regarding this Kosmos, in the short run, they suggest that relativistic dissipative fluids (or magnetofluids) and relativistic continuous media play an important role in astrophysical-and also subnuclear-scales. This realization brings into the frontiers of current research theories of irreversible thermodynamics of relativistic continuous media. Motivated by these considerations, we summarize the progress that has been made in the last few decades in the field of nonequilibrium thermodynamics of relativistic continuous media. For coherence and completeness purposes, we begin with a brief description of the balance laws for classical (Newtonian) continuous media and introduce the classical irreversible thermodynamics (CIT) and point out the role of the local-equilibrium postulate within this theory. Tangentially, we touch the program of rational thermodynamics (RT), the Clausius–Duhem inequality, the theory of constitutive relations and the emergence of the entropy principle in the description of continuous media. We discuss at some length, theories of non equilibrium thermodynamics that sprang out of a fundamental paper written by Müller in 1967, with emphasis on the principles of extended irreversible thermodynamics (EIT) and the rational extended irreversible thermodynamics (REIT). Subsequently, after a brief introduction to the equilibrium thermodynamics of relativistic fluids, we discuss the Israel–Stewart transient (or causal) thermodynamics and its main features. Moreover, we introduce the Liu–Müller–Ruggeri theory describing relativistic fluids. We analyze the structure and compare this theory to the class of dissipative relativistic fluid theories of divergent type developed in the late 1990 by Pennisi, Geroch and Lindblom. As far as theories of nonequilibrium thermodynamics of classical media are concerned, it is fair to state that substantial progress has been made and many predictions of the extended theories have been placed under experimental scrutiny. However, at the relativistic level, the situation is different. Although the efforts aiming to the development of a sensible theory (or theories) of nonequilibrium thermodynamics of relativistic fluids (or continuous media) spans less than a half-century, and even though enormous steps in the right direction have been taken, nevertheless as we shall see in this review, still a successful theory of relativistic dissipation is lacking.

General thermodynamic efficiency loss, aging and Gompertz mortality law

A simple and general thermodynamic theory is applied to describe the irreversible aspects of the continuous process of functional efficiency loss, which occurs in dissipative biological structures after they reach maturity [1]. This theory, among other things, follows Prigogine [2] by considering that these dissipative structures perform their functions and carry out cyclical processes per se since they are self-organizing away from equilibrium. By using the irreversible thermodynamic theory of aging by Montemayor-Aldrete et al [1], we have obtained results such as the following: The accumulated damage that occurs in dissipative biological structures after they reach maturity, which is the product of linear loss of functional efficiency with time, leads to the law of exponential mortality rate by Gompertz. The average solar power volumetric density of frequency ν dissipated by circular molecules of radius , which reside on the inner surface of some lipid vesicles that float in the Archean oceans and that contain water and other chemical components are obtained. Such expression resembles the Stefan–Boltzmann law which describes the power radiated from a black body in terms of its temperature. Also, an expression for the volumetric density of the average entropy production rate by molecules of radius is obtained. Finally, the coupling processes that occur between the matter and heat fluxes between the interior and the exterior of lentil-shaped lipid vesicles pumped by the solar radiation action are analyzed qualitatively as well as their possible consequences in relation to the prebiotic chemical evolution of dissipative systems that can give rise to life.

FEM Implementation of the Coupled Elastoplastic/Damage Model: Failure Prediction of Fiber Reinforced Polymers (FRPs) Composites

The coupled damage/plasticity model for meso-level which is ply-level in case of Uni-Directional (UD) Fiber Reinforced Polymers (FRPs) is implemented. The mathematical formulations, particularly the plasticity part, are discussed in a comprehensive manner. The plastic potential is defined in effective stress space and the damage evolution is based on the theory of irreversible thermodynamics. The model which is illustrated here has been implemented by different authors previously but, the complete pre-requisite algorithm ingredients used in the implicit scheme implementation are not available in the literature. This leads to the complexity in its implementation. Furthermore, this model is not available as a built-in material constitutive law in the commercial Finite Element Method (FEM) softwares. To facilitate the implementation and understanding, all the mathematical formulations are presented in great detail. In addition, the elastoplastic consistent operator needed for implementation in the implicit solution scheme is also derived. The model is formularized in incremental form to be used in the Return Mapping Algorithm (RMA). The quasi-static load carrying capability and non-linearity caused by the collaborative effect of damage and plasticity is predicted with User MATerial (UMAT) subroutine which solves the FEM problem with implicit techniques in ABAQUS.

The Thermodynamics of Relativistic Multi-Fluid Systems

This article extends the single-fluid relativistic irreversible thermodynamics theory of Muller, Israel andStewart (hereafter the MIS theory) to a multi-fluid system with inherent species interactions. This is illustratedin a two-fluid toy-model where an effective complex 4-velocity plays the role of a primary dynamicalparameter. We find that an observer who resides in the real-part of this universe will notice that theirknowledge of the universe parametrized using real, rather than imaginary, quantities are insufficient to fullydetermine properties such as the total energy density, pressure or entropy, In fact, such an observer willdeduce the existence of some negative energy that affects the expansion of their perceived real universe.

The Thermodynamics of Relativistic Multifluid Systems

This article extends the single-fluid relativistic irreversible thermodynamics theory of {\it M{\"u}ller}, {\it Israel} and {\it Stewart} (hereafter the {MIS} theory) to a multi-fluid system with inherent species interactions. This is illustrated in a two-fluid toy-model where an effective complex 4-velocity plays the role of a primary dynamical parameter. We find that an observer who resides in the {\it real}-part of this universe will notice that their knowledge of the universe parametrized using {\it real}, rather than {\it imaginary}, quantities are insufficient to fully determine properties such as the total energy density, pressure or entropy, In fact, such an observer will deduce the existence of some negative energy that affects the expansion of their perceived {\it real} universe.

Relativistic Theory of Irreversible Thermodynamics for Multi-Component Fluids and Its Post-Newtonian Limit in Relation to Classical Extended Thermodynamics

Abstract First, the special-relativistic Theory of Irreversible Processes for a multi-component fluid is formulated. It is based on (i) the balance equations of the particle number and the energy-momentum for the total system (i. e., the mixture of the components) as well as the sub-systems (i. e., the components) and (ii) the dissipation inequality and the Gibbs equation for the mixture. In order to allow for reactions between the single components, in contrast to the total system, the sub-systems are assumed to be open, which means that their particle number and energy-momentum are not constrained by conservation laws. Without making any assumptions on the thermodynamic behavior of the interacting components, one arrives at a thermodynamic description of the mixture showing now heat conduction and viscosity. In particular, this makes it possible to calculate the entropy production and, thus, to identify thermodynamic currents and forces. In a second part, the post-Newtonian limit of this theory is calculated to show that for the mixture there result relations known from classical Extended Thermodynamics that partly are corrected by entrainment terms. The mathematical origin and physical consequences of these terms are discussed.

Thermodynamically Consistent Methodology for Estimation of Diffusivities of Mixtures of Guest Molecules in Microporous Materials.

The Maxwell–Stefan (M–S) formulation, that is grounded in the theory of irreversible thermodynamics, is widely used for describing mixture diffusion in microporous crystalline materials such as zeolites and metal–organic frameworks (MOFs). Binary mixture diffusion is characterized by a set of three M–S diffusivities: Đ1, Đ2, and Đ12. The M–S diffusivities Đ1 and Đ2 characterize interactions of guest molecules with pore walls. The exchange coefficient Đ12 quantifies correlation effects that result in slowing-down of the more mobile species due to correlated molecular jumps with tardier partners. The primary objective of this article is to develop a methodology for estimating Đ1, Đ2, and Đ12 using input data for the constituent unary systems. The dependence of the unary diffusivities Đ1 and Đ2 on the pore occupancy, θ, is quantified using the quasi-chemical theory that accounts for repulsive, or attractive, forces experienced by a guest molecule with the nearest neighbors. For binary mixtures, the same occupancy dependence of Đ1 and Đ2 is assumed to hold; in this case, the occupancy, θ, is calculated using the ideal adsorbed solution theory. The exchange coefficient Đ12 is estimated from the data on unary self-diffusivities. The developed estimation methodology is validated using a large data set of M–S diffusivities determined from molecular dynamics simulations for a wide variety of binary mixtures (H2/CO2, Ne/CO2, CH4/CO2, CO2/N2, H2/CH4, H2/Ar, CH4/Ar, Ne/Ar, CH4/C2H6, CH4/C3H8, and C2H6/C3H8) in zeolites (MFI, BEA, ISV, FAU, NaY, NaX, LTA, CHA, and DDR) and MOFs (IRMOF-1, CuBTC, and MgMOF-74).

Thermodynamics and evolutionary biology through optimal control

We consider a particular instance of the lift of controlled systems proposed in the theory of irreversible thermodynamics and show that it is equivalent to a variational principle for an optimal control in the sense of Pontryagin. Then we focus on two important applications: in thermodynamics and in evolutionary biology. In the thermodynamic context, we show that this principle provides a dynamical implementation of the Second Law, which stabilizes the equilibrium states of a system. In the evolutionary context, we show that our principle leads directly to the Optimal Replicator Equation, and we discuss several interesting features: it provides a robust scheme for the coevolution of the population and its fitness landscape; it has a clear formulation in terms of an optimization process; and finally, it extends standard evolutionary dynamics to include phenomena such as the emergence of cooperation.