In thermodynamics schools, the Brussels school of thermodynamics is a school of thermodynamic logic, born in 1918, centered around the work of mathematician and physicist Théophile de Donder and his noted student Russian-born Belgian chemist Ilya Prigogine at the Free University of Brussels, a university now divided between the French-speaking Université Libre de Bruxelles and the Dutch-speaking Vrije Universiteit Brussel. [1] The term "Brussels school" came into use in the 1950s. The following is a 1991 summary of the Brussels school by Ching-yao Hsieh and Meng-Hua Ye: [7]

“The inherent wholeness of atomic process also give impetus to the emerging new paradigm of the ‘self-organizing’ principle expounded by the so-called ‘Brussels school’ under the leadership of Ilya Prigogine, the Nobel Prize laureate of 1977.”

American writer Alan Toffler summarizes the main ideas of the Brussels school as follows: [8]

(a) The Newtonian mechanistic world view concerns itself mostly with closed systems and linear relationships. But the phenomena of high-technology industrial societies of today are open systems in which information and innovation are the critical resources.
(b) All systems contain subsystems that are continually fluctuating. The order and organization of the existing system will be shattered when the fluctuations become very powerful. The critical point has been called the ‘bifurcation point’ It is impossible to determine in advance which direction change will take.
(c) Order and organization can arise spontaneously out of chaos through a ‘self-organization process.’

This ‘self-organizing principle’, as conceived, introduces an optimistic arrow of time model into the universe, in contrast to the colloquial pessimistic arrow of time of movement towards increasing disorder. [7]

Synonyms include the: Belgian school, Brussels school of irreversible thermodynamics, Prigogine school, or Prigogine school of non-equilibrium thermodynamics, Brussels school of thermodynamic chemistry, among others.

De Donder
In 1899, Théophile de Donder received his doctorate in physics and mathematics from the Université Libre de Bruxelles, for a thesis entitled Sur la Théorie des Invariants Intégraux (On the Theory of Integral Invariants). [2] He was professor between 1911 and 1942, at the Université Libre de Bruxelles. Initially he continued the work of Henri Poincaré and Elie Cartan. As from 1914 he was influenced by the work of Albert Einstein and was an enthusiastic proponent of the theory of relativity.

In 1918, the “birth year” of the Brussels school, the then 45 years old de Donder began to devote his time to superior teaching, after he was for some years appointed as a secondary school teacher, on the nature of thermodynamics. At this time, he was promoted to professor at the Department of Applied Science, and began without delay the writing of a course on theoretical thermodynamics for engineers. [4]

Starting with Clausius’ second principle of thermodynamics, having been formulated as an inequality: "uncompensated heat" is positive - or, in more recent terms, entropy production is positive, where the inequality refers, of course, to phenomena that are irreversible, as are any natural processes, de Donder, in the words of Prigogine, extracted the entropy production out of this ‘sfumato’ when related it in a precise way to the pace of a chemical reaction, through the use of a new function that he was to call ‘affinity’. [5] In his approach, de Donder gave a new formulation of the second principle, based on such concepts as affinity and degree of evolution of a reaction, considered as a chemical variable. [4] He gained significant reputation in 1923, when he developed his definition of chemical affinity. He pointed out a connection between the chemical affinity and the Gibbs free energy.

Russian-born Belgian Ilya Prigogine, one of de Donder's students, obtained both his undergraduate and graduate education in chemistry at the Free University of Brussels, receiving his first doctoral degree in 1941 and later becoming a professor in 1950. [4] A second teacher of thermodynamics influential to Prigogine, at the Brussels school, was Jean Timmermans (1882-1971) an experimentalist, especially interested in the applications of classical thermodynamics to liquid solutions, and in general to complex systems, in accordance with the approach of the great Dutch thermodynamics school of Johannes van der Waals and Bakhuis Roozeboom. [6]

In 1954, Prigogine, together with Raymond Defay, published Treatise on Thermodynamics: Based on the Methods of Gibbs and De Donder. [3] Five years later, in 1959, Prigogine was appointed director of the International Solvay Institute in Brussels, Belgium. In that year he also started teaching at the University of Texas at Austin in the United States, where he later was appointed Regental Professor and Ashbel Smith Professor of Physics and Chemical Engineering. In 1967 he co-founded there what is now called The Center for Complex Quantum Systems. In that year he also returned to Belgium where he became director of the Center for Statistical Mechanics and Thermodynamics.

Norwegian-born American physical chemist Lars Onsager is often said to be a proponent or associated with the Prigogine school or view. Greek-born Belgian physicist Grégoire Nicolis was a graduate student of Prigogine, later co-writting several human thermodynamics themed books with him.

A notable human thermodynamics student of Prigogine, via his University of Texas affiliation, is Dick Hammond.

1. Mishra, R.K. (1989). Molecular and Biological Physics of Living Systems, (pg. 81). Taylor & Francis.
2. De Donder, Théophile. (1899). Sur la Théorie des Invariants Intégraux (On the Theory of Integral Invariants) Acad. Roy. Belg., Bull. Cl. Sc., page 169, 1968.
3. Prigogine, Ilya and Defay, Raymond. (1954). Treatise on Thermodynamics: Based on the Methods of Gibbs and De Donder. Longmans, Green.
4. Autobiography (Ilya Prigogine) -
5. De Donder, Theophile. (Rédaction nouvelle par P. Van Rysselberghe), Paris, Gauthier- Villars, 1936.
6. (a) Timmermans, J., Les Solutions Concentrées, Masson et Cie, Paris, 1936.
(b) see also: his thesis on experimental research on demixtion in liquid mixtures.

7. Hsieh, Ching-Yao, and Ye, Meng-Hua. (1991). Economics, Philosophy, and Physics (pg. 108). M.E. Sharpe.
8. Toffler, Alan. (1894). “Introduction”, in: Order Out of Chaos: Man’s New Dialogue with Nature (by Ilya Prigogine and Isabella Stengers). Bantam Books.

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