# Herbert Callen

Herbert Bernard Callen (July 1, 1919 – May 22, 1993) was an American physicist specializing in thermodynamics and statistical mechanics.[1] He is considered one of the founders of the modern theory of irreversible thermodynamics,[2] and is the author of the classic textbook Thermodynamics and An Introduction to Thermostatistics, published in two editions.[3] During World War II, his services were invoked in the theoretical division of the Manhattan Project.[3]

Herbert Bernard Callen
BornJuly 1, 1919
DiedMay 22, 1993
Merion, Pennsylvania
CitizenshipUnited States
Alma materTemple University
Massachusetts Institute of Technology
Known forFluctuation-dissipation theorem
Thermodynamics and An Introduction to Thermostatistics (1960, 1985)
Scientific career
FieldsThermodynamics
Statistical mechanics
InstitutionsUniversity of Pennsylvania
ThesisOn the Theory of Irreversible Processes (1947)
Doctoral studentsThomas Kaplan

## Life and work

A native of Philadelphia, Herbert Callen received his Bachelor of Science degree from Temple University.[4] His graduate studies were interrupted by the Manhattan Project. He also worked on a U.S. Navy project concerning guided missiles (Project Bumblebee) at Princeton University in 1945.[2] Callen subsequently completed his PhD in physics at the Massachusetts Institute of Technology (MIT) in 1947. He was supervised by the physicist László Tisza. His doctoral dissertation concerns the Kelvin thermoelectric and thermomagnetic relations, and Onsager's reciprocal relations;[2] it was titled On the Theory of Irreversible Processes.[5] Upon receiving his degree, Callen spent a year at the MIT Laboratory for Insulation Research and developed his theory of electrical breakdown for insulators.[2]

In 1948, Callen joined the faculty of the Department of Physics at the University of Pennsylvania and became a professor in 1956.[6] Specialists consider his most lasting contribution to physics to be the paper co-written with Theodore A. Welton presenting a proof of the fluctuation-dissipation theorem, an extremely general result describing how a system's response to perturbations relates to its behavior at equilibrium.[3] This crucial result became the basis for the statistical theory of irreversible processes and explains how fluctuations dissipate energy into heat in general[6] and the phenomenon of Nyquist noise in particular.[2] Callen then pioneered the thermodynamic Green's functions for magnetism. With his students, he studied many-body problems involving spin operators. This led to the discovery of some useful methods of approximations.[2]

The first edition of his classic text Thermodynamics and An Introduction to Thermostatistics was published in 1960.[3] In it, he presents a rigorous axiomatic treatment of thermodynamics in which the state functions are the fundamental entities and the processes are their differentials.[2] The postulates concern the existence of thermal equilibrium, and the properties of entropy. From them, he derives the fundamentals of thermodynamics, found in the first eight chapters.[7] The much revised second edition, published in 1985, became a highly cited reference in the literature[2] and an enduring textbook.[7]

He was a successful teacher, noted for his ability to explain complicated phenomena in simple terms. He played a key role in the recruitment of promising solid-state physicists to the University of Pennsylvania in the late 1950s and continued to be active in the University's academic affairs till his retirement in 1985.[2]

He was the recipient of a Guggenheim Fellowship for the academic year 1972-1973.[8] In 1984, Callen received the Elliott Cresson Medal from the Franklin Institute. He retired in 1985.[3] He was made a member of the National Academy of Sciences in 1990.[9]

After battling Alzheimer's disease for eleven years, Herbert Callen died in the Philadelphia suburb of Merion in 1993. He was 73 years old. He was survived by his wife, Sara Smith, and their two children, Jed and Jill.[3] According to the Center for Disease Control and Prevention (CDC), Alzheimer's remained a leading cause of death in the United States in 2016.[10]

## Textbook

• Callen, Herbert B. (1985). Thermodynamics and an Introduction to Themostatistics (2nd ed.). New York: John Wiley & Sons. ISBN 0-471-86256-8.

• Part I: General Principles of Classical Thermodynamics
• Introduction: The Nature of Thermodynamics and the Basis of Thermostatistics
• Chapter 1: The Problem and the Postulates
• Chapter 2: The Conditions of Equilibrium
• Chapter 3: Some Formal Relationships, and Sample Systems
• Chapter 4: Reversible Processes and the Maximum Work Theorem
• Chapter 5: Alternative Formulations and Legendre Transformations
• Chapter 5: The Extremum Principle in the Legendre Transformed Representations
• Chapter 7: Maxwell Relations
• Chapter 8: Stability of Thermodynamic Systems
• Chapter 9: First-order Phase Transitions
• Chapter 10: Critical Phenomena
• Chapter 11: The Nernst Postulate
• Chapter 12: Summary of Principles for General Systems
• Chapter 13: Properties of Materials
• Chapter 14: Irreversible Thermodynamics
• Part II: Statistical Mechanics
• Chapter 15: Statistical Mechanics in the Entropy Representation
• Chapter 16: The Canonical Formalism; Statistical Mechanics in Helmholtz Representation
• Chapter 17: Entropy and Disorder; Generalized Canonical Formulations
• Chapter 18: Quantum Fluids
• Chapter 19: Fluctuations
• Chapter 20: Variational Properties, Perturbation Expansions, and Mean Field Theory
• Part III: Foundations
• Chapter 21: Postlude: Symmetry and the Conceptual Foundations of Thermostatistics
• Appendix A: Some Relations Involving Partial Derivatives
• Appendix B: Magnetic Systems
• General References
• Index

### Assessment

Front cover of the second edition.

Robert B. Griffiths, a specialist in thermodynamics and statistical mechanics at the Carnegie Mellon University, commented that both editions of this book presents clearly and concisely the core of thermodynamics within the first eight chapters. At the time of writing (1987), Griffiths knew of books that explained the principles of thermodynamics, but Callen's was had the best presentation of the material. He believed Callen offered a pedagogical, if abrupt, treatment of the subject. His book begins in an abstract manner, assuming the existence and properties of entropy and derive the consequences for various processes of interest rather than through heat engines and thermodynamic cycles or by statistical mechanics and Boltzmann's entropy formula ${\displaystyle S=k\ln \Omega }$ . However, he argued that Callen's treatment of critical phenomena (Chapter 10) contains some technical flaws. Callen thought that classical analysis had broken down. But Griffiths wrote that the problem lies not in the breakdown of thermodynamics but rather the Taylor-expansion of thermodynamic quantities, and that precise expressions of the functions appearing in a fundamental relation should be determined by statistical mechanics and experiments, not thermodynamics. Nevertheless, Griffiths still believed this book to be an excellent resource for learning the basics of thermodynamics.[11]

According to L.C. Scott, who studied statistical mechanics and biophysics at Oklahoma State University, Thermodynamics and an Introduction to Thermostatistics is a popular textbook that begins with some basic postulates based on intuitive classical, empirical, and macroscopic arguments. He found that it is remarkable for the whole edifice of classical thermodynamics to follow from just a few basic assumptions. However, Scott preferred the discussion of temperature in Heat and Thermodynamics by Mark W. Zemansky and Richard H. Dittman because it is based on thermometry and forces students to contemplate the empirical basis of concept of temperature, leaving aside the molecular basis of heat. He argued that such an approach yields greater appreciation for the meaning of temperature and its statistical-mechanical basis which students will encounter later. In contrast, Callen's book does not mention temperature till Chapter 2, where Callen defines temperature as the reciprocal of the derivative of entropy with respect to internal energy then shows, using the postulates, that this definition is consistent with our intuition. While Zemansky and Dittman cover the first law of thermodynamics empirically, Callen simply assumes the existence of the internal energy function the invokes the conservative nature of inter-atomic forces. Whereas Zemansky and Dittman treated the second law of thermodynamics using heat engines and simply state the Clausius and Kelvin formulations of it, in Callen's book, the second law is contained within the postulates. Scott was unsure which approach is more understandable for students. In general, Zemansky and Dittman employed an empirical approach while that of Callen is deductive. Scott opined that Zemansky and Dittman's book is more suitable for beginning students while Callen's is more appropriate for an advanced course or as a reference.[7]

## References

1. ^ "Herbert B. Callen" (biography). College Park, Maryland: American Institute of Physics, retrieved online February 23, 2019.
2. Burstein, Elias; Cohen, Michael; Harris, A. Brooks; Lubensky, Tom C. (August 1994). "Obituary: Herbert B. Callen". Physics Today. 47 (8): 74–75. Bibcode:1994PhT....47h..74B. doi:10.1063/1.2808620. Archived from the original on 2013-10-05. Cite uses deprecated parameter |deadurl= (help)
3. "Obituary: Herbert B. Callen, 73, Theoretical Physicist". The New York Times. May 27, 1993. Retrieved May 30, 2019.
4. ^ Callen, Herbert Bernard, Biographies, The Lower Merion Historical Society
5. ^ "Herbert Callen - The Mathematics Genealogy Project". Mathematics Genealogy Project. Department of Mathematics, North Dakota State University. Retrieved June 21, 2019.
6. ^ a b "Herbert B. Callen". Member Directory. National Academy of Sciences. Retrieved August 31, 2019.
7. ^ a b c Scott, L. C. (February 1998). "Thermodynamics and An Introduction to Thermostatistics, 2nd ed". American Journal of Physics. 66 (2): 164–7. doi:10.1119/1.19071.
8. ^ "Herbert B. Callen". John Simon Guggenheim Memorial Foundation. Retrieved June 21, 2019.
9. ^ "Biography: Herbert B. Callen". American Institute of Physics. Retrieved May 30, 2019.
10. ^ "Leading Causes of Death". Center for Disease Control and Prevention. March 17, 2017. Retrieved June 21, 2019.
11. ^ Griffiths, Robert B. (September 1987). "Thermodynamics and An Introduction to Thermostatistics". American Journal of Physics. 55 (5): 860–1. doi:10.1119/1.14986.