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 - 3.6 MB)# (PS - 4.5 MB)
Continuation of the previous reference.
Joseph-Louis Lagrange (1736-1813)
Edwin T. Jaynes (1922-1998) biography, photograph, bibliography from G. Larry Bretthorst
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.
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)