Elementary Principles of Statistical Mechanics

by Josiah Willard Gibbs

Elementary Principles of Statistical Mechanics: Large Print By J. Willard Gibbs This book was originally published prior to 1923, and represents a reproduction of an important historical work, maintaining the same format as the original work. While some publishers have opted to apply OCR (optical character recognition) technology to the process, we believe this leads to sub-optimal results (frequent typographical errors, strange characters and confusing formatting) and does not adequately preserve the historical character of the original artifact. We believe this work is culturally important in its original archival form. While we strive to adequately clean and digitally enhance the original work, there are occasionally instances where imperfections such as blurred or missing pages, poor pictures or errant marks may have been introduced due to either the quality of the original work or the scanning process itself. We are delighted to publish this classic book as part of our extensive Classic Library collection. Many of the books in our collection have been out of print for decades, and therefore have not been accessible to the general public. The aim of our publishing program is to facilitate rapid access to this vast reservoir of literature, and our view is that this is a significant literary work, which deserves to be brought back into print after many decades. The contents of the vast majority of titles in the Classic Library have been scanned from the original works. To ensure a high quality product, each title has been meticulously hand curated by our staff. Our philosophy has been guided by a desire to provide the reader with a book that is as close as possible to ownership of the original work. We hope that you will enjoy this wonderful classic work, and that for you it becomes an enriching experience.

Genres: Physics, Science

272 pages, Paperback

First published January 1, 1981

About the author

Josiah Willard Gibbs (February 11, 1839 – April 28, 1903) was an American scientist who made important theoretical contributions to physics, chemistry, and mathematics. His work on the applications of thermodynamics was instrumental in transforming physical chemistry into a rigorous deductive science. Together with James Clerk Maxwell and Ludwig Boltzmann, he created statistical mechanics (a term that he coined), explaining the laws of thermodynamics as consequences of the statistical properties of large ensembles of particles. Gibbs also worked on the application of Maxwell's equations to problems in physical optics. As a mathematician, he invented modern vector calculus (independently of the British scientist Oliver Heaviside, who carried out similar work during the same period).

In 1863, Yale awarded Gibbs the first American doctorate in engineering. After a three-year sojourn in Europe, Gibbs spent the rest of his career at Yale, where he was professor of mathematical physics from 1871 until his death. Working in relative isolation, he became the earliest theoretical scientist in the United States to earn an international reputation and was praised by Albert Einstein as "the greatest mind in American history". In 1901 Gibbs received what was then considered the highest honor awarded by the international scientific community, the Copley Medal of the Royal Society of London, "for his contributions to mathematical physics".

Commentators and biographers have remarked on the contrast between Gibbs's quiet, solitary life in turn of the century New England and the great international impact of his ideas. Though his work was almost entirely theoretical, the practical value of Gibbs's contributions became evident with the development of industrial chemistry during the first half of the 20th century. According to Robert Andrews Millikan, in pure science Gibbs "did for statistical mechanics and for thermodynamics what Laplace did for celestial mechanics and Maxwell did for electrodynamics, namely, made his field a well-nigh finished theoretical structure."

Reviews

[Colin Lamont · Rating 5 out of 5]

Years into grad school I still couldn't understand this ensemble business, canonical or otherwise. In fact, I really didn't understand thermodynamics or statistical mechanics at all. It became a procrastinatory outlet of mine to go into the uni library and take out books on stat mech and try and level up as a physicist in understanding this stuff. I worked through Pathria, Prigogine, Landau, (Oliver) Penrose, Fermi, Feynman, Ma. Several of them mentioned Gibbs, and on a whim, I purchased this book from Abebooks. It was imported from India and printed with exceptionally poor quality. It cost me about 2 dollars, shipping included. I thought I might read it for historical value.

What I can't get over is that it simply is the best book on stat mech. It is an absolute gem, I actually came away from reading this book really, FINALLY, understanding. The clarity of mind, the creativity of the proofs, the elegance of the chosen equations... what monumental physical insight this man had! It would be enough if this were simply A textbook on stat mech.

However. It happens to be the Origin of Species for Stat mech, single-handedly completing the science to a degree which seems inhumanly prophetic. There is not one single thing in this book which relativity and quantum mechanics or anything else in 117 years has done to invalidate. It is a true testament to the power of human imagination to see into the heart of nature.

For it to be BOTH a historic and pedagogical miracle, for it to be both practically and poetically living in my life as a scientist, I mean how many stars can I give? How much gratitude is too much? I rave about this book to people I barely know. Gibbs is the paradigmatical American scientist: a practical, clear, creative mind---a diamond chisel cutting perfection from the incomprehensible.

The value of this book cannot be overstated. To history (modern chemistry, electronics, .... ), to physics (stat mech, probability theory, the importance of phase space, the quantum groundwork), and finally, to me and my career as a Gibbsian acolyte. If you do physics, you MUST read it.

[William Bies · Rating 3 out of 5]

Josiah Willard Gibbs, active at Yale University from 1871 to 1903, was one of the earliest American scientists to secure an international reputation. His fame today rests upon his work on the statistical mechanical basis of physical chemistry, summed up in his Elementary Principles in Statistical Mechanics (originally published in 1902, reprinted here by the Ox Box Press in 1981). Now, Gibbs may be credited with 1) coming up with the idea of an ensemble itself; 2) that the ensemble exists in phase space; 3) that the value of any measurable quantity of interest should be given by an ensemble average of an appropriate function of phase space. The familiar terms of art, microcanonical, canonical and grand canonical ensembles were coined in this work by Gibbs, though the concepts themselves can certainly be found in Ludwig Boltzmann’s works.

What impresses one upon revisiting this slender memoir is how far Gibbs is able to get in realizing his stated aim of erecting an independent, that is statistical foundation for the discipline otherwise known as classical thermodynamics (for a good modern representative of the more traditional approach to the subject one may consult Herbert B. Callen’s Thermodynamics and an Introduction to Thermostatistics, John Wiley, 1985). The advantage of the present work over, say, Maxwell and Boltzmann’s original papers lies in its apparent simplicity and systematicity. The new concepts introduced are clearly explained (considering the state of mathematics at the time) and the calculations actually carried out are all fairly elementary. Notable contributions include the Gibbs free energy (hence, the very concept of a chemical potential) and his eponymous phase rule. Nonetheless, in the present work Gibbs does not stray beyond the equilibrium domain or entertain irreversible processes at all; there is no transport theory and no H-theorem, his considerations on the establishment of equilibrium are purely heuristic.

Thus, we assign three stars: too abstract, there are no worked examples, and not quite as original as it may seem prima facie if one knows Boltzmann’s work. The design of the present work fails to be ample enough to do justice to Gibbs’ own major contributions to physical chemistry and classical thermodynamics, as contained in his published memoirs. Still, an illuminating read, if only to gain a sense of how far one can get in formulating a rational foundation to thermodynamics in classical mechanics which nowadays must be deemed to have been supplanted by the more sophisticated techniques of quantum statistical mechanics. If one is looking for more than just a sense of what can be accomplished along the lines Gibbs sketches here, either in the classical or in the quantum case, this reviewer would recommend turning to another standby textbook for more substantial fare, namely Terrell L. Hill’s Statistical Mechanics: Principles and Selected Approaches (McGraw-Hill, 1956, now out in a convenient Dover reprint).