This video is the second of two lectures in this unit.

Instructors: Prof. Paul Penfield, Prof. Seth Lloyd

## Resources

### Technical

The person most responsible for use of maximum entropy principles in various fields of science is Edwin T. Jaynes. The seminal papers are:

Jaynes, E. T. "Information Theory and Statistical Mechanics." *Physical Review* 106 (May 15, 1957): 620-630. (PDF - 2.1 MB)^{#} (PS - 2.5 MB)

This paper started the modern use of the Principle of Maximum Entropy in physics.

———. "Information Theory and Statistical Mechanics II." *Physical Review* 108 (October 15, 1957): 171-190. (PDF - 3.8 MB)^{#} (PS - 4.5 MB)

Continuation of the previous reference.

Jaynes, E. T. "Information Theory and Statistical Mechanics." In *Statistical Physics*. 1962 Brandeis Lectures in Theoretical Physics, Volume 3. New York, NY: W. A. Benjamin, Inc., 1963. pp. 181-218. (PDF)^{#} (PS - 1.1 MB)

Another good explanation, in terms of estimating probabilities of an unfair die.

Personal history by Jaynes, Edwin T. "Where Do We Stand on Maximum Entropy?" In *The Maximum Entropy Formalism*. Edited by Raphael D. Levine and Myron Tribus. Cambridge, MA: MIT Press, 1978. pp. 15-118. ISBN: 9780262120807. (PDF - 2.5 MB)^{#} (PS - 3.2 MB)

### Historical

Joseph-Louis Lagrange (1736-1813)

Ludwig Boltzmann (1844-1906)

Cercignani, Carlo. *Ludwig Boltzmann, The Man Who Trusted Atoms*. Oxford, UK: Oxford University Press, 2006. ISBN: 9780198570646.

Biography of Ludwig Boltzmann, an Austrian physicist who was a pioneer in thermodynamics and entropy.

On Boltzmann's tombstone (closeup) is the formula for entropy "S = k log W".

Friedrichs, Brian J. Ludwig Edouard Boltzmann. Another Ludwig Boltzmann biography.

Truesdell, C. *The Tragicomical History of Thermodynamics, 1822 - 1854*. Berlin, Germany: Springer-Verlag, 1980. ISBN: 9780387904030.

History of the twisted and convoluted development of the difficult concept of entropy. Professor Truesdell died January 14, 2000 at the age of 80. He retired from the faculty at Johns Hopkins University in 1989.

Edwin T. Jaynes (1922-1998) biography, photograph, bibliography from G. Larry Bretthorst

### Books

There are many textbooks on thermodynamics and energy conversion.

Silbey, R., R. Alberty, and M. Bawendi. *Physical Chemistry*. New York, NY: John Wiley & Sons, 2004. ISBN: 9780471215042.

These authors are from MIT. Alberty was formerly Dean of Science, and Silbey was until recently Dean of Science. It's amazing that anyone can be a Dean and still keep up with science.

Zemansky, Mark W. *Heat and Thermodynamics*. 3rd ed. New York, NY: McGraw-Hill, 1951, or earlier editions starting in 1937.

Typical excellent book in a traditional style. This book does not mention information, and starts with assumed knowledge about temperature, pressure, and volume. Suitable for advanced undergraduates.

Van Ness, H. C. *Understanding Thermodynamics*. New York, NY: Dover Publications, 1969.

Introductory book, used for sophomores, covering classical thermodynamics (no information). Succinct and carefully crafted treatment.

Callen, Herbert B. *Thermodynamics*. New York, NY: John Wiley & Sons, 1962.

Book covering both equilibrium and irreversible thermodynamics.

Truesdell, C. *Rational Thermodynamics*. New York, NY: McGraw-Hill, 1969.

Careful treatment of classical thermodynamics (no mention of information) with emphasis on the mathematical formalism. Suitable for graduate courses, for those with some prior exposure to thermodynamics.

White, David C., and Herbert H. Woodson. *Electromechanical Energy Conversion*. New York, NY: John Wiley & Sons, 1959.

Textbook developed at MIT in energy conversion (no thermodynamics).

Tribus, M. *Thermostatics and Thermodynamics*. Princeton, NJ: D. Van Nostrand Co, Inc., 1961.

An early textbook to use the Principle of Maximum Entropy as an approach to thermodynamics. The philosophy of assuming maximum uncertainty is discussed in Chapter 3.