Books Review by B.Ramesh

2012 年 3 月 9 日 コメントをどうぞ コメント

A Historical Approach to Entropy . Collected papers of Eri Yagi and her coworkers
186 + 72 pp. supplement , figs. , tables , bibl.
Tokyo :International Publishing Institute , 2002.

The late Clifford Truesdell once observed that “The workshop of the scholar in the history of science is the periods in which his authors lived. He should know those periods’ ways of life and belief and education, both the common and the eccentric; their political histories; their variety in aspects; their social and economic structures; their architectures, literatures, and arts. He should feel at home in the houses of those times, sit easily in their chairs, both figurative and wooden, and discern what was then mostly admired or rejected in painting and sculpture and decoration. He should have read not only the books that carried the intellectual products of his period but also those that were then the fare of young minds as they were taught, such books having been commonly of an earlier time. The student who does not command, as a minimum, the main episodes of Holy Scripture, classic mythology, and the corpus of golden Latin is glaucomatose in the modes of thought of Western men educated before 1900”. (The scholar: A species threatened by professions .C Truesdell – Critical Inquiry, 1976 ).
The expectations of Truesdell , as set out in the above quotation , are extremely demanding indeed and many would be daunted by the very thought of historical enquiry. It is thus deeply satisfying that Prof. Eri Yagi has fearlessly plunged herself into the world of Rudolph Clausius to illumine an important chapter in the history of thermodynamics . Prof. Eri Yagi and her co-workers have been immersed in the thought of Clausius for over 30 years now. Beginning with a paper in Historia Scientarium in 1981, Prof. Yagi has been consistently chipping away at the work of Clausius .A diverse array of approaches that include the methods of text analysis , mathematical equation analysis through creating a database of about 500 equations from Clausius’s 16 papers on the mechanical theory of heat , analysis of experimental tables used by Clausius , and the data mining approach of technical term analysis have been brought to bear on the task. In coming to terms with Clausius , Prof. Eri Yagi and her team have had to grapple with the German language as well.
The book under notice , published on the occasion of her retirement in 2002 , begins with a useful synoptic overview of their oeuvre and contains besides 5 other papers by her team. Also included are an English translation of Clausius’s 1947 [1847 by editor] paper on light propagation , a list of Clausius’s publications , and a list of Prof. Eri Yagi’s publications.
The two lists of publications on thermodynamics and statistical mechanics that are also included ought to interest researchers wishing to pursue the history of these controversial subjects.

Classical phenomenological thermodynamics and its sister discipline statistical mechanics continue to be dogged by controversy . The infinitesimals of Clausius and thermodynamics have mystified many mathematicians and scientists. J.B. Diaz remarks , for example , that his chemistry professor would illustrate the notion of an infinitesimal amount of pressure by holding up “his right hand in front of the class , with the tips of his thumb and index finger very close together”. (J.B.Diaz , Siam Review , April 1978. Mathematical prologemena to every theory of homogeneous heat engines ).
Despite the confusing use of the term ” complete differential ” by Clausius , Prof. Yagi is able to delve into the mathematics of Clausius and show that for a reversible process , in the mathematical expression of the first law, dU, the internal energy was treated similarly to dS , the change in entropy . Prof. Yagi also shows that Clausius realized that the heat of a body depends on the path of changes during a process and that Clausius’s grasp of analytical mechanics could have led him to the realization that dQ is a non-perfect differential. The work of Gaspard Monge and the science of mechanics had treated the condition of integrability for differential equations and Clausius was familiar with this work. The authors also bring out the influence of J.Fourier upon Clausius’s mathematical derivation of the first law. Clausius modified Clapeyron’s approach by focusing on the heat expended that included a second order differential term .
By an examination of the experimental tables used by Clausius , the authors show that while he was not an experimental physicist himself , he nevertheless made skillful use of experimental data from other researchers like Clapeyron , Regnault , Thomson etc. Clausius found several values of 1/A (ratio = work produced / heat expended) and showed an agreement with Joule’s equivalent of work for unit heat .This reassured Clausius that his approach in combining Carnot’s theory with Joule’s principle was correct.
Through a technical term analysis of Clausius’s 12th paper of 1853 the authors bring out the influence upon Clausius of prominent physicists such as Helmholtz , Poggendorff , Peltier , Thomson etc. They express the hope that such an approach could help people who do not know the German language.
The above details are a partial and somewhat inadequate summary of the richly textured and layered work of the authors. While no author can satisfy every whim and fancy of a reviewer , some areas which piqued the interest of this reviewer and left him groping for answers are outlined next.
Truesdell used the epithet “Heraclitean ” to describe Clausius. Pierre Duhem stressed that ” It is necessary that it [science] treat not only change of place in space but also all movement of alteration , of generation and of corruption …Thermodynamics is the new science , whose construction appears to be the great work of physicists of the nineteenth century , for it embraces all these kinds of changes …it is truly the physics for which Aristotle sketched general outlines , but it is the physics of Aristotle developed and made precise by efforts of experimentalists and mathematicians .” (p 221 , Science in the provinces: scientific communities and provincial leadership leadership in France, 1860-1930 , Mary Jo Nye , University of California Press , 1986). Duhem also drew sharp attention to the fact that Clausius was careful not to mix his phenomenoligal approach with his molecular theories of the second law. Prof. Sambursky has also traced the roots of thermodynamics to ancient Greek thought. However , Clausius was heir to a tradition wherein the study of Aristotlean views was in decline .By 1752 at Freiburg University , for example , it was “absolutely prohibited” to include in physics “the unfounded teachings(which cannot be confirmed by experience)” of Aristotle (p 24 footnote , Intellectual Mastery of Nature. Theoretical Physics from Ohm to Einstein , Volume 1 … Christa Jungnickel, Russell McCormmach , University of Chicago Press, 1990 ).
Other scholars have also in recent times called for a redirection of science to broader Aristotlean notions of change . More recently , Prof. Kozo Mayumi along with Mark Glucina have drawn attention to the fact that it is important to look at the qualitative aspects of entropy for some fields at least — ” it is a solid understanding of the laws themselves, rather than the mathematics, that provides insights relevant to economics .” ( Glucina, M. D. and Mayumi, K. (2010) , Connecting thermodynamics and economics. Annals of the New York Academy of Sciences, 1185: 11–29 ).
The question that arises then is to what extent was Clausius influenced by the mechanistic temper of his times in seeking an explanation of entropy in terms of molecular motions. Willard Gibbs even regarded Clausius as the father of statistical mechanics , a subject which continues to echo the challenges thrown at it by Loschmidt , Zermelo , Poincare
and others. Some scholars claim that Clausius came up with molecular ideas such as disgregation in order to preempt William Rankine from claiming credit for a fundamental explanation of the notion of entropy.
Several writers have pointed out that the idea of decline and decay was very much in the air when Rankine, Clausius , and Thomson came up with the general idea of entropy. Thomson even resorted to Biblical imagery to describe the notion of dissipation of energy. Prof. Barri Gold has even argued that poet laureate Alfred Tennyson anticipated the scientists as regards the second law ! It would be interesting to find out if Clausius was influenced by these general notions of decay and decline in coming up with his ponderous statement : Die Entropie der Welt strebt einem Maximum zu.

The historian Professor Russell McCormmach once said “When I want to understand something, I invariably look to see how it came about in time, that is, I study it through its history…I study not only how science has changed in time but also how the rest of the world has changed with it…I use different approaches: I write history to depict the working relationships of large numbers of scientists, biography to deal with the experience of a particular scientist, and fiction to get at the meaning of science in individual lives.” (http://aps.org/units/fhp/awards/pais/index.cfm ).
Given the sparseness of historical information about Clausius , his views on religion etc. , Prof. Eri Yagi may even have to try her hand at fiction in order to answer questions such as the ones above ! But given the verve and tenacity displayed by her thus far a broader approach is surely not an impossible task.
Finally , it may not be out of place to draw attention to the fact that Prof. Eri Yagi came to historical studies — from a solid academic grounding in physics — owing to her reservations about nuclear technologies and radiation concerns.
Her vision ,post Fukushima , appears almost prophetic in nature. It is also interesting that there appears to be a link between thermodynamics and the substantial quantities of waste heat dumped into the ocean by nuclear power reactors. While this quantity of waste heat may be very small in comparison to the vast store of heat energy in the ocean , the accumulation of such waste heat over long spans of time could release additional amounts of carbon dioxide from the oceans into the atmosphere . (Among others , Kozo Mayumi and Takashi Hirose have raised such concerns ). Thus not only radiation fears but also the spectre of climate change serve to undermine the so-called “green” image of nuclear power.