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The talk explores the origins of modern mathematical physics in Kyiv and provides an overview of M. Bogolyubov's manuscripts created at the Institute of Mathematics.
Note that the Institute of Mathematics officially admitted M. Bogolyubov as a senior researcher on March 1, 1945. On April 1, he assumed the head of the Department of Asymptotic Methods and Statistical Mechanics. The dismissal order, dated November 1, 1956, was signed by Yu.O. Mitropolsky, who was then the deputy acting director of the institute, and O.S. Parasyuk. However, M. Bogolyubov's fate was intertwined with the Institute long before. He was a student of Professor D.O. Grave, who founded the Institute of Mathematics at the Ukrainian Academy of Sciences in March 1920. From the age of thirteen, M. Bogolyubov became a participant in the well-known mathematical seminar of D.O. Grave. Under its influence, he is forming as a scientist in the field of mathematical and theoretical physics. Later in June 1925, at the request of D.O. Grave, the Small Presidium of Ukrgolovnauka decided to consider M. Bogolyubov as a graduate student of the research department of mathematics in Kyiv. In 1928, he defended his doctoral dissertation.
In his renowned monograph "Problems of Dynamic Theory in Statistical Physics", which was a manuscript of a report for 1945 at the Institute of Mathematics in Kyiv, M. Bogolyubov formulated a consistent approach to the problem of deriving kinetic equations from the dynamics of many particles. Using perturbation theory methods, a strategy was developed for constructing a generalization of the Boltzmann equation, known as the Bogolyubov kinetic equation, and for the first time, other kinetic equations were substantiated. This work clarified the mechanism of irreversibility in the evolution of many-particle systems, whose dynamics are described by time-reversible fundamental evolution equations. These results were extended to quantum many-particle systems. In particular, in his pioneering work, the superfluidity phenomenon was first described by the quantum kinetic equation.
The ideas generated by Bogolyubov at the Institute of Mathematics have laid the groundwork for the theory of kinetic equations and have become the cradle of modern statistical mechanics, as recognized today.