7R21. Nonequilibrium Thermodynamics: Transport and Rate Processes in Physical and Biological Systems. - Y Demirel (Dept of Chem Eng, VPI, 127 Randolph Hall, Blacksburg VA 24061). Elsevier Sci BV, Amsterdam, Netherlands. 2002. 420 pp. ISBN 0-444-50886-4. \$210.00.

Reviewed by S Sieniutycz (Dept of Chem and Process Eng, Warsaw Univ of Tech, 1 Warynskiego St, Warsaw, 00-645, Poland).

The book is, in fact, a volume for readers primarily interested in life sciences (physiology, biology, medicine, etc) or related fields, where insight is more important than exactness, at least initially. Formally, a broader audience has been assumed for the book by the publisher: graduate students and researchers working in the areas of physics, chemistry, biology, chemical engineering, biochemical engineering and biomedical engineering. Yet, especially in teaching students of physics and theoretical chemistry, the use of more rigorous treatments such as the classical textbook by De Groot and Mazur will be necessary. In addition, the book contains introductory information on several new growing applied branches of non-equilibrium thermodynamics (for example: applications of entropy and the second law in chemical engineering, exergy balancing, thermoeconomics, coupling systems theory, bioenergetics in mitochondria, active transport, etc).

The book attempts to give the reader a broad, updated review of applications of the theory of nonequilibrium processes. To warrant the self-contained structure of the volume, two preparatory chapters are included of which the first is on equilibrium thermodynamics and the second on transport and rate processes. The basic intention of the author seems to be to bring together many important developments in irreversible thermodynamics of recent years at an elementary level, and thereby render them accessible to a broad audience of beginners. The book extends the range of applied topics covered in earlier treatments of the subject by including some contemporary applications which are still at the research stage.

The goals and contents of the book along with basic historical aspects of the discipline are defined in the Preface (a Foreword, actually). The content is organized reasonably, thus a beginner finds a relatively simple and transparent picture of the field. Chapter 1 is on equilibrium thermodynamics. It describes basic definitions, reversible and irreversible processes, equilibrium, thermodynamic laws, entropy and entropy production, the Gibbs equation, equations of state, and thermodynamic potentials. The brief review of classical issues is done well. Yet the sections on thermodynamic potentials and extremum properties are somewhat inconclusive. Chapter 2 is on transport and rate processes. It introduces nonequilibrium systems and outlines such issues as: kinetic approach, transport phenomena, the Maxwell-Stefan equations, transport coefficients, electric charge flow, the thermal relaxation theory, preliminaries on chemical reactions and coupled processes.

Chapter 3 deals with linear nonequilibrium thermodynamics. Its sections discuss local thermodynamic equilibrium, second law of thermodynamics, phenomenological equations, Curie-Prigogine principle, dissipation function, and variation of entropy production. Chemical affinity A appears in Section 3 (satisfying the convention that the affinity is positive when the reaction rate is positive), and the limiting linear formulas in this section are consistent with this convention. This chapter serves to prepare the reader to understand why the proportionality between A and the reaction rate J can be assumed in linear descriptions. In discussing this particular chapter, it seems especially appropriate to recall that the elementary nature of the book does not release its author from the satisfaction of a certain degree of rigor and completeness. Unfortunately, the degree of oversimplification and incompleteness in this material is so large that the text often resembles careless lecture notes. In the text devoted to the local equilibrium assumption no discussion on the effect of time (spatial) scales is included, and the role of Knudsen’s number is not considered. The nonequilibrium nature of Gibbs equation is not discussed. The notion of dissipation function in the force representation is identified in Section 5 (modulo to the temperature factor) with that of the entropy production. In general, no sharp distinction is made between the bilinear structures describing entropy production and quadratic functions of dissipation.

Chapter 4 is on balance equations and entropy generation in continua where field description is applied and partial differential equations are suitable in the thermodynamic description. Basic equations are obtained by the standard procedure that combines the conservation laws for mass, energy and momentum into the internal energy equation. Next, with the help of the Gibbs equation, the internal energy equation is transformed into an equation describing the entropy balance, with the entropy production term. In Eq. (63) of this chapter chemical affinity A appears defined (as in earlier sections) subject to the convention that the affinity is positive when the reaction proceeds from left to right. Unfortunately, however, in an unnumbered equation above Eq. (63) the chemical reaction term is obtained with an incorrect sign, and this error is repeated in the subsequent work, causing misunderstandings.

Chapter 5 deals with (nonequilibrium) entropy and exergy. Outlined are principles of the exergy balance, and the (Gouy-Stodola) law is recalled which links the exergy degraded with the entropy production. Approximate equations are given that describe exergies of some special systems, yet without clear specification of underlying assumptions. Preliminary information is given about the role of exergy concept in description of biological systems, calculation of exergy efficiencies and ecological applications of exergy, to characterize depletion of natural resources.

Chapter 6 continues the application of the second law of thermodynamics by presenting examples with convection and heat flow in ducts and packed systems, where minimizing the entropy generation leads to information about the optimum size of equipment. In particular, heat and mass exchangers are analyzed, and Tondeur’s and Kvaalen’s “principle of equipartition of the entropy production” or related “equipartition of forces” (uniformly distributed entropy generation rate or uniform forces) is discussed in some detail. The equipartition of forces is not properly explained and, perhaps, not properly understood. This is not a surprise because no such thing exists, except for some strictly linear systems. In fact, as proved by Eqs. (90) and (95) of the chapter, even for the simple process of Fourier heat conduction it is rather grad(lnT) or $T−1$ gradT than grad T itself that is constant along an optimal path. Summing up, one must be contented that at least the final result of the analysis based on the literature material (Tondeur’s and Kvaalen’s publication [54]) is presented in a correct form. Chemical reactions, reacting flows and separation operations are next analyzed following a group of (sloppy or incorrect) approaches whose purpose is the extension of (correct) Tondeur’s and Kvaalen’s principle to nonlinear processes. These approaches principally follow the group of research papers written by Sauar and Ratkje-Kjelstrup and their coworkers, refs. [33,39,40].

In Chapter 7, thermoeconomics is introduced. Distinction between purely thermodynamic optimization and approaches leading to thermoeconomic optima is analyzed. Availability and exergy destruction number are discussed in the context of exchaustion of nonrenewable resources and ecological costs. Equipartition and optimization are treated following the techniques similar to those applied in Chapter 6.

In Chapter 8, molecular diffusion phenomena are treated with the help of Maxwell-Stefan frictional model. Next, diffusion in non-electrolyte systems is compared with diffusion in electrolyte systems. For those latter, the role of chemical potentials of electroneutral combinations and the Gibbs equation written in terms of electrically neutral species is pointed out. Irreversible processes in electrolyte systems are described in terms of electrochemical affinities along with diffusion and conductivity coefficients, transferrence numbers and corresponding mobilities. In Chapter 9, coupled processes of heat and mass transfer are treated along with classical issues such as thermal diffusion (Soret effect) and the Dufour effect of the heat flow caused by a concentration gradient. Heat of transport, entropy of transport and degree of coupling are defined. Coupling in binary liquid mixtures is extensively treated with special attention paid to the L Rowley experiments.

Chapter 10 deals with thermodynamic aspects of chemical and biochemical reactions. Again, within the same chapter, some formulas are correct for chemical affinities defined positively [eg, Eqs. (1), (12), (13)], and the others—for affinities defined as negative quantities [eg, Eqs. (2) and (3)]. Still they are formulas in which both conventions of A must be used to make them correct, see, eg, Eq. (10) and Eq. (42) supplemented by the affinity definition below that is inconsistent with it. Very nice for true lovers of thermodynamics! Dissipation for chemical reactions, Michaelis-Menten kinetics and coupled chemical reactions can still be considered.

In Chapter 11, the classical information on membrane transport is based primarily on the research of Katchalsky and his coworkers. Passive transport, electrokinetic effects, facilitated transport and active transport are reviewed. Chapter 12 brings valuable newer information on thermodynamics and biological systems. It describes mitochondria and related bioenergetics, oxidative phosphorylation, and identification of proper pathways in a vicinity of reference steady states far from equilibrium. Further information is on multiple inflection points, coupling in mitochondria, Stucki linear approximation, coupling variation, and thermodynamic regulation in bioenergetics. Considerable portion of the text is devoted to facilitated transport, active transport, molecular evolution, and molecular machines. Classical evolutionary criterium is linked with Tellegen’s theorem known for network systems. Chapter 13 discusses some other thermodynamic approaches amongst of which are network thermodynamics with bond graph, mosaic nonequilibrium thermodynamics and rational thermodynamics.

Chapter 14 is devoted to extended nonequilibrium thermodynamics, yet the thermodynamic stability conditions it adduces are classical. It also outlines ordering in physical and biological structures and bifurcations in Bernard cells. Extended nonequilibrium thermodynamics in the commonly understood sense, ie, as the theory based on the Gibbs equation extended by the presence of dissipative fluxes, is considered in the last section of the chapter.

In recent decades, thermodynamics has attained a remarkable level of competence in advanced design of practical devices, complex energy and industrial systems, bioprocesses, chemical reactors, reacting flows, separations, and even (most recently) flying objects. One of the key concepts of nonequilibrium thermodynamics is that it can take account of dynamic behavior and pathwise constraints. Some recent developments in thermodynamics, aimed at extending the range of its application to far-from equilibrium regimes (extended thermodynamics, only briefly discussed in the book) abandon the assumption of local equilibrium. Consequently problems in nonequilibrium thermodynamics are formulated as typical or extended macroscopic problems of thermodynamic networks or fields. New developments consider also various aspects of material structure, in particular polymeric fluids and rheological bodies described by general rheological equations of state and bodies with continuous spectra. Still other developments stress similarities of the field with the theory of bifurcating and chaotic systems. In the last decade, an intense activity has been modifying and improving our understanding of statistical mechanics and thermodynamics, and extending its applicability to small and non-extensive systems, systems exhibiting violations of the standard ergodic and mixing properties, or other anomalies. Also, important developments in the connection between statistical mechanics and dynamical systems theory have produced a new understanding of the properties of macroscopic systems. In fact, none of these newer topics is discussed in the book in question. The book represents one of traditional approaches; it describes phenomena at macroscopic level leaving out some recent evergreen problems such as catastrophes, statistical disequilibria and chaos, although many applications can be found there as well. In spite of all its shortcomings, the book reviewed is one of a few books on nonequilibrium phenomena written to date that penetrates the subject matter in a simple way, yet giving a broad overview of contemporary applications.

Nonequilibrium Thermodynamics is the one of the rare books to provide a vast treatment bringing together many advances in the applications within the field. The treatment is largely self-contained and provides a unified perspective on those applied problems which are beyond the realm of conventional analytical and computational techniques of engineering sciences. Moreover, this treatment includes many of the unifying properties and simplifications discovered in recent research. Nonequilibrium Thermodynamics summarizes these new applications of thermodynamics as tools that can be used in thermodynamically optimal designs and in understanding diverse phenomena in natural processes.

As scientific rigor is not a basic virtue of this book, the number of errors, inconsistencies, and typos is remarkable. Nonequilibrium Thermodynamics: Transport and Rate Processes in Physical and Biological Systems is not free of flaws, but it is an ambitious, inspiring and timely book, a treatise giving a broad overview of nontrivial applications available to date only in research papers, a book which may be read by researchers and graduate students interested in concise presentation of the theory and exhaustive treatment of applications, including those in biological systems. The book is well edited in terms of organization, technical writing, and the use of illustrations; it is also attractively printed. As this is a book of considerable didactic quality, in spite of its shortcomings, it is worth reading.