In thermodynamics schools, the MaxEnt school or “maximum entropy school of thermodynamics”, sometimes called the Janes school, is a school of thought centered around a combination of the maximum entropy principle, information theory, statistical thermodynamics, Gibbsian thermodynamics, and the 1957 two part paper “Information Theory and Statistical Thermodynamics” of American physicist Edwin Jaynes, in which an attempt was made to derive a statistical thermodynamics interpretation of information theory. [1] American engineer Myron Tribus, who is connected with the MIT school of thermodynamics, is a co-founder of the MaxEnt school of logic.

Etymology
The demarcation of a Jaynes school seems to have arisen via the 1994 paper “Foundations of Non-equilibrium Statistical Mechanics” by English theoretical physicist John Dougherty, who opened his paper to the view that there exist two separate “schools”, one based on subdynamics the other on information theory, on which the general foundation of non-equilibrium statistical mechanics can be based on. In coining the name of the latter school, Dougherty stated: [7]

“The second school, which we shall refer to as the 'Maxent school', is that associated with Professor ET Jaynes and his collaborators.”

In the years to follow, this began to be modified to MaxEnt, with a capital E, or maximal (or maximum) entropy school.

Overview
The maximum entropy school, supposedly, was launched in 1957: [6]

“The MaxEnt school of thermodynamics initiated with two papers published in the Physical Review by Edwin Jaynes in 1957.”

The “MaxEnt theory”, MaxEnt approach, MaxEnt view, or MaxEnt formulation of nonequilibrium statistical thermodynamics, is a logic which is said to consist of an algorithm involving the maximization of Shannon information entropy, subject to the constraints imposed by the available information. [2] Other terms often used to describe the teachings or theory of this school of thought include "MaxEnt workshops", "MaxEnt models", etc.

The Janes school is sometimes said to be intertwined with Bayesian-methods, the statistics and probability methods of English mathematician Thomas Bayes: [7]

“Jaynes has been accused of exaggerating the differences between the 'orthodox' probability school—Fisher and frequentist company—and his MaxEnt school of Bayesian/Laplacian revivalists.”

The following 2004 quote gives an in context synopsis of the subject: [2]

“How is it that Jayne’s MaxEnt formulation of nonequilibrium statistical mechanics has for so long failed to be accepted by the majority of scientists when the logic of it is precisely that of Boltzmann and Gibbs? Part of the answer lies with the relative paucity of published results from the MaxEnt school, especially with regard to the new testable predictions far-from-equilibrium.”

The idea expressed here is that Prigoginean thermodynamics methods are published and tested in far greater numbers than are Jayne's methods. The following 2001 quote gives another inside perspective of the MaxEnt school:

“A great deal of work has been done, notably by Jaynes and his school, in an attempt to justify the maximum entropy principle, but we cannot say that we are any closer to such a justification today than Boltzmann or Szilard ever were.”

This quote here is referring to the 1872 effort of Austrian physicist Ludwig Boltzmann, in his "Further Studies on the Thermal Equilibrium of Gas Molecules", to justify the increase of entropy on probability arguments, particularly via his H-theorem interpretation of entropy as the velocity distribution of particles, and the the later 1929 attempt of Hungarian physicist Leo Szilard, in his On the Decrease in Entropy in a Thermodynamic System by the Intervention of Intelligent Beings, to connect information to entropy using Maxwell demon arguments.

Jaynes
In his 1957 two-paper “Information Theory and Statistical Thermodynamics”, American physicist Edwin Jaynes attempted to connect equilibrium thermodynamics, with the statistical mechanics (or statistical thermodynamics) of American engineer Willard Gibbs, with information interpretations. [3]

Tribus
Connected with the MaxEnt school is American engineer Myron Tribus, who learned of Janes' work in 1958, after he had been struggling for ten years with the supposed problem as to explain the connection between the entropy of Clausius and the entropy of Shannon, after being asked this question during is doctoral dissertation examination at UCLA.

In 1959, the year after he read Jaynes' paper, which he considered to be his Rosetta stone, Tribus invited Jaynes to come to UCLA to participate in a two week summer course on information theory and thermodynamics, during which time Tribus learned that Jaynes had been preparing material for a book on probability and its applications; the taught the course together. Although Jaynes never completed his book, Tribus did writing his 1961 Thermostatics and Thermodynamics: an Introduction to Energy, Information and States of Matter, based, as he says, “squarely on Ed’s work”; the fundamental ideas in this book taken directly from Jaynes’ work, which was never published. Tribus could only cite Jaynes’ work as “in print”. Tribus' book was the first book publication to attempt to base the laws of thermodynamics on information theory rather than on the classical arguments.

In April 1961, Tribus gave a seminar at MIT on a new way to derive thermodynamics based on information theory. He states that a critical audience, comprised of students of American mechanical engineer Joseph Keenan, founder of the MIT school of thermodynamics, “tried to rip it apart”. Moreover, French mathematician Benoit Mandelbrot was in the audience and quickly attacked the MaxEnt interpretation, saying: “Everyone knows that Shannon’s derivation is in error.”

Beyond this, it happened that information theory founder Claude Shannon was in residence at MIT that week, so Tribus went to see him. Shannon, according to Tribus, “was immediately able to dispel Mandelbrot’s criticism, but went on to lecture me on his misgivings about using his definition of entropy for applications beyond communication channels.” [4]

Perspective of
This school is generally rejected by main stream thermodynamicists as an unfounded mathematical contrivance, on the basis that American electrical engineer Claude Shannon's famous 1948 "A Mathematical Theory of Communication" has absolutely nothing to do with thermodynamics.

Into the 2000s, Jaynes' MaxEnt formulation of nonequilibrium statistical thermodynamics has generally failed to be accepted by the majority of scientists. [5]

Outside of thermodynamics proper, however, there are seem to be numerous practitioners of this school who seem to unassumingly maintain that their theories are based on the second law of thermodynamics.

References
1. Crapo, Henry H., Rota, Gian-Carlo, Senato, D. (2001). Algebraic Combinatorics in Computer Science, (pg. 73). Springer.
2. Kleidon, Axel and Lorenz, Ralph D. (2004). Non-equilibrium Thermodynamics and the Production of Entropy: Life, Earth, and Beyond (pg. 42). Springer.
3. (a) Jaynes, E. T. (1957) “Information theory and statistical mechanics”, (PDF), Physical Review 106:620.
(b) Jaynes, E. T. (1957) “Information theory and statistical mechanics II”, (PDF), Physical Review 108:171.
4. Tribus, M. (1998). “A Tribute to Edwin T. Jaynes”. In Maximum Entropy and Bayesian Methods, Garching, Germany 1998: Proceedings of the 18th International Workshop on Maximum Entropy and Bayesian Methods of Statistical Analysis (pgs. 11-20) by Wolfgang von der Linde, Volker Dose, Rainer Fischer, and Roland Preuss. 1999. Springer.
5. Kleidon, Axel and Lorenz, Ralph D. (2004). Non-equilibrium Thermodynamics and the Production of Entropy: Life, Earth, and Beyond (pg. 42-43). Springer.
6. Anon. (2008). Predicting: Webster’s Quotations, Facts and Phrases (MaxEnt school, pgs. 369, 342; quote cited as [WP] meaning of Wikipedia origin). Icon Group International.
7. Dougherty, John P. (1994). “Foundations of Non-equilibrium Statistical Mechanics” (abstract), Phil Trans R Soc Lond, A346:259-305.
8. Toffoli, Tommaso. (2004). “Maxwell’s demon, the Turing Machine, and Jayne’s robot”; published as “Honesty in Inference”, American Scientist, 92:92):182-85.