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September 8, 2008
Volume 86, Number 36
pp. 42-43

Thermodynamics Extended

Far-from-equilibrium thermodynamics is at the heart of many real systems and processes

Reviewed by Raymond Kapral

THERMODYNAMICS is one of the most successful theories of matter ever constructed. There are no known violations of the theory for the description of macroscopic systems for which it was devised. But despite its remarkable success, thermodynamics is limited to systems at or near equilibrium.

Thermodynamics and Fluctuations far from Equilibrium,
by John Ross, Springer, 2008, 210 pages, $159 hardcover (ISBN: 978-

Researchers would like to be able to use thermodynamics to describe the properties of systems that are far from equilibrium, because such systems are the rule rather than the exception in nature. For example, they may want to use thermodynamics to compute the efficiency of a proton pump in a living system or an engine operating with maximum power output. Scientists would also like a thermodynamic function that describes the evolution of a system to a nonequilibrium steady state or one that determines the relative stabilities of multiple steady states.

Generalizing thermodynamics to treat such nonequilibrium situations is the subject matter of "Thermodynamics and Fluctuations far from Equilibrium," by John Ross. Because nonequilibrium thermodynamics lies at the heart of many and diverse real processes, the book's subject matter should prove useful to a wide audience including, among others, physicists, chemists, biologists, and engineers.

The basic formulation of thermodynamics as scientists now use it dates from the 19th century and rests primarily on the work of Sadi Carnot, Rudolf Clausius, William Thomson (Lord Kelvin), and Josiah Willard Gibbs. Thermodynamics grew out of the need to solve practical problems in engineering. As its name implies, it was constructed to deal with heat and mechanical work, concepts that originally were not well defined.

Carnot's objective was to determine the maximum amount of work that can be derived from a given amount of heat. His investigation of this problem led to an understanding of the role of cyclic and reversible processes in the conversion of heat to work and in the efficiency of heat engines.

The work of Clausius and Kelvin led to the precise formulations of the second law, which restricts the types of heat engines that are possible and introduces the condition for spontaneity in isolated systems. Gibbs extended these concepts to transformations between all forms of energy.

For systems near equilibrium, linear irreversible thermodynamics is well founded and based on the concept of local equilibrium. However, almost all mechanical devices in daily use operate far from equilibrium. Furthermore, current technological advances are often based on the nanoscale properties of materials. Similarly, biological systems as a rule operate under far-from-equilibrium conditions, and biochemical processes in the cell occur on mesoscopic scales. In such cases, fluctuations affect the properties of the system, and the standard formulations of thermodynamics do not apply. Generalizing thermodynamics to encompass such situations is challenging and remains an active area of research to this day.

THE BOOK addresses these issues from a personal perspective that describes the work of Ross and his collaborators in this area. The author makes no attempt to review all the contributions of other investigators, as he states in the introduction. Instead, the book is a compendium of Ross's contributions to this field over a period of more than 30 years.

The book consists of three parts: thermodynamics and fluctuations in systems that lie far from equilibrium, dissipation and efficiency in this regime, and general aspects of fluctuations in systems that are far from equilibrium. Its central focus is chemically reacting systems under far-from-equilibrium conditions.

One of the characteristic features of thermodynamics is that it provides conditions for spontaneity. For example, a well-known condition is that entropy will increase in a spontaneous process occurring in an isolated system. It has been an important goal to generalize such statements for systems that are constrained to lie far from equilibrium, in either steady or more complicated system states.

This is one of the problems the book tackles. In this connection, the study of the effects of fluctuations on far-from-equilibrium dynamics enters the story because fluctuations can determine whether criteria for spontaneity exist in such systems. This discussion is especially important because it is now recognized that in small systems, both physical and biological, such fluctuations affect how they operate.

The first several chapters develop the basic ideas underlying the development of thermodynamics for chemically reacting systems that lie far from equilibrium. In particular, the chapters introduce and compare descriptions of thermodynamic and stochastic master equations. And they discuss the important issue of constructing spontaneity criteria for nonequilibrium steady states. Appealing aspects of these chapters are that they illustrate theoretical results by simple model examples and also provide or suggest calculations and experimental tests of the theory of thermodynamics for far-from-equilibrium systems.

THE SECOND PART of the book views these issues from a perspective not often utilized in standard texts—one that considers real rather than idealized heat engines. Here, the author considers the power and efficiency of thermal engines from a point of view that explicitly includes dissipative terms. He discusses conditions that lead to maximum power and methods for computing the efficiency of engines at maximum power.

The book also shows how the periodic supply of reagents to chemical and biochemical reacting systems can influence their behavior. For example, using small changes in experimental conditions obtained by periodically varying the input of reagents, one can control the degree of dissipation in oscillatory chemical reaction networks.

Discussions of the efficiency and power of engines naturally lead to considerations of "finite-time thermodynamics" in a chapter written by R. Stephen Berry, an emeritus professor of chemistry at the University of Chicago. Although traditional approaches to irreversible thermodynamics usually are based on the notion of local equilibrium, here Berry considers processes that occur in finite time. The development of this topic, like the discussions of efficiency and power in previous chapters, aims to improve the performance of real engines. The author derives conditions for the existence of potential-like quantities and discusses design properties of engines when power rather than efficiency is maximum.

The far-from-equilibrium domain is not often covered in standard treatments of thermodynamics, although the topic is slowly finding its way to graduate and undergraduate courses. This book is a welcome contribution to the topic.

Raymond Kapral is a professor of chemistry at the University of Toronto.

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