Department of Electrical Engineering and Computer Science
 Department of Mechanical Engineering
 6.050J / 2.110J     Information and Entropy     Spring 2003


Unit 10: Energy


Lecture Tuesday, Apr 29, 2003, 12:00 PM Room 37-212
Recitation Thursday, May 1, 2003, 12:00 PM Room 37-212
Problem Set Posted Friday, Apr 25, 2003 Due Friday, May 2, 2003
Solutions Posted Friday, May 2, 2003  

Lecture Handouts

Students who for any reason did not receive these items can pick up a copy in Room 38-344. Most of this material is also available on the 6.050J/2.110J Web site

Reading Assignment

  • 6.050J / 2.110J notes, Energy



Seminal papers on the Principle of Maximum Entropy by Edwin T. Jaynes (July 5, 1922 - April 30, 1998):

  • Jaynes, E. T., "Information Theory and Statistical Mechanics," Physical Review, vol. 106, no. 4, pp. 620-630; May 15, 1957. PDF (2.2 MB), PS (2.6 MB). This paper started the use of the Principle of Maximum Entropy in physics
  • Jaynes, E. T., "Information Theory and Statistical Mechanics. II," Physical Review, vol. 108, no. 2, pp. 171-190; October 15, 1957. PDF (2.2 MB), PS (2.6 MB). Continuation of the previous reference
  • The philosophy of assuming maximum uncertainty is discussed in Chapter 3 of M. Tribus, "Thermostatics and Thermodynamics," D. Van Nostrand Co, Inc., Princeton, NJ; 1961
  • Another good explanation, in terms of estimating probabilities of an unfair die is in E. T. Jaynes, "Information Theory and Statistical Mechanics," pp. 181-218 in "Statistical Physics," Brandeis Summer Institute 1962, W. A. Benjamin, Inc., New York, NY; 1963. PDF, PS
  • Personal history by Jaynes, Edwin T. Jaynes, "Where Do We Stand on Maximum Entropy?," pp. 15-118, in "The Maximum Entropy Formalism," Raphael D. Levine and Myron Tribus, editors, The MIT Press, Cambridge, MA; 1979. PDF, PS


  • Joseph-Louis Lagrange biography
  • Biography of Ludwig Boltzmann, Austrian physicist, 1844-1906, who was a pioneer in thermodynamics and entropy, is Carlo Cercignani, "Ludwig Boltzmann, The Man Who Trusted Atoms," Oxford University Press, Oxford, UK; 1998.
  • On Boltzmann's tombstone is the formula for entropy "S = k log W"
  • Ludwig Boltzmann biography
  • Another Ludwig Boltzmann biography
  • History of the twisted and convoluted development of the difficult concept of entropy, C. Truesdell, "The Tragicomical History of Thermodynamics, 1822 - 1854," Springer-Verlag, Berlin; 1980. 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 biography, photograph, bibliography


There are many textbooks on thermodynamics and energy conversion.

  • R. Silbey and R. Alberty, "Physical Chemistry," Wiley; 2001. These authors are from MIT. Alberty was formerly Dean of Science, and Silbey is now Dean of Science. It's amazing that anyone can be a Dean and still keep up with science.
  • Typical excellent book in a traditional style, Mark W. Zemansky, "Heat and Thermodynamics," McGraw-Hill Book Company, Inc., New York, NY; Third Edition, 1951, or earlier editions starting in 1937. This book does not mention information, and starts with assumed knowledge about temperature, pressure, and volume. Suitable for advanced undergraduates.
  • Introductory book, used for sophomores, covering classical thermodynamics (no information), H. C. Van Ness, "Understanding Thermodynamics," Dover Publications, New York, NY; 1969. Succinct and carefully crafted treatment.
  • Book covering both equilibrium and irreversible thermodynamics, Herbert B. Callen, "Thermodynamics," John Wiley and Sons, Inc., New York NY; 1962.
  • Careful treatment of classical thermodynamics (no mention of information) with emphasis on the mathematical formalism, C. Truesdell, "Rational Thermodynamics," McGraw-Hill Book Company, New York, NY; 1969. Suitable for graduate courses, for those with some prior exposure to thermodynamics.
  • Textbook developed at MIT in energy conversion (no thermodynamics), David C. White and Herbert H. Woodson, "Electromechanical Energy Conversion," John Wiley and Sons, Inc., New York, NY; 1959.
  • An early textbook to use the Principle of Maximum Entropy as an approach to thermodynamics is M. Tribus, "Thermostatics and Thermodynamics," D. Van Nostrand Co, Inc., Princeton, NJ; 1961

Help Wanted

6.050J/2.110J students: be the first to suggest a resource, for example a useful Web site or a good book or article, to add to the list above. If your suggestion is accepted by the 6.050J/2.110J staff, you will get a $5 ice-cream gift certificate. Send your suggestion by e-mail during Spring 2003 to 6.050-staff at

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