Nikolay Sergeevich Krylov (; 10 August 1917 – 21 June 1947) was a

Soviet The Union of Soviet Socialist Republics. (USSR), commonly known as the Soviet Union, was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 until Dissolution of the Soviet ...

theoretical physicist Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain, and predict natural phenomena. This is in contrast to experimental physics, which uses experi ...

known for his work on the problems of

classical mechanics Classical mechanics is a Theoretical physics, physical theory describing the motion of objects such as projectiles, parts of Machine (mechanical), machinery, spacecraft, planets, stars, and galaxies. The development of classical mechanics inv ...

statistical physics In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applicati ...

, and

quantum mechanics Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...

.. He showed that a sufficient condition for a

dynamical system In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space, such as in a parametric curve. Examples include the mathematical models ...

to relax to equilibrium is for it to be mixing.

Biography

Krylov was born in

Ustyuzhna Ustyuzhna () is a types of inhabited localities in Russia, town and the administrative center of Ustyuzhensky District in Vologda Oblast, Russia, located on the Mologa River, west of Vologda, the administrative center of the oblast. Population: ...

Vologda Governorate Vologda Governorate (), also known as the Government of Vologda, was an administrative-territorial unit (''guberniya'') of the Russian Empire and the Russian Soviet Federative Socialist Republic, Russian SFSR, which existed from 1796 until 1929. ...

, of the

Russian Empire The Russian Empire was an empire that spanned most of northern Eurasia from its establishment in November 1721 until the proclamation of the Russian Republic in September 1917. At its height in the late 19th century, it covered about , roughl ...

. He graduated in physics from the

Leningrad University Saint Petersburg State University (SPBGU; ) is a public university, public research university in Saint Petersburg, Russia, and one of the oldest and most prestigious universities in Russia. Founded in 1724 by a decree of Peter the Great, the uni ...

. He then was a

doctoral student A doctorate (from Latin ''doctor'', meaning "teacher") or doctoral degree is a postgraduate academic degree awarded by universities and some other educational institutions, derived from the ancient formalism ''Licentiate (degree), licentia docendi' ...

in the

theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain, and predict List of natural phenomena, natural phenomena. This is in contrast to experimental p ...

group supervised by

Vladimir Fock Vladimir Aleksandrovich Fock (or Fok; ) (December 22, 1898 – December 27, 1974) was a Soviet physicist, who did foundational work on quantum mechanics and quantum electrodynamics. Biography He was born in St. Petersburg, Russia. In ...

, and wrote thesis on the foundations of

statistical mechanics In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applicati ...

entitled '' Mixing processes in

phase space The phase space of a physical system is the set of all possible physical states of the system when described by a given parameterization. Each possible state corresponds uniquely to a point in the phase space. For mechanical systems, the p ...

'' awarded by for the degree of

Candidate of Science A Candidate of Sciences is a PhD-equivalent academic research degree in all the post-Soviet countries with the exception of Ukraine, and until the 1990s it was also awarded in Central and Eastern European countries. It is officially classified ...

in 1941. During the

German invasion of the Soviet Union Operation Barbarossa was the invasion of the Soviet Union by Nazi Germany and several of its European Axis allies starting on Sunday, 22 June 1941, during World War II. More than 3.8 million Axis troops invaded the western Soviet Union along a ...

and the

Siege of Leningrad The siege of Leningrad was a Siege, military blockade undertaken by the Axis powers against the city of Leningrad (present-day Saint Petersburg) in the Soviet Union on the Eastern Front (World War II), Eastern Front of World War II from 1941 t ...

, Krylov was assigned to the air defense of the city. He continued research work at

Kazan Kazan; , IPA: Help:IPA/Tatar, ɑzanis the largest city and capital city, capital of Tatarstan, Russia. The city lies at the confluence of the Volga and the Kazanka (river), Kazanka Rivers, covering an area of , with a population of over 1. ...

for the Physical-Technical Institute of the

Academy of Sciences of the Soviet Union The Academy of Sciences of the Soviet Union was the highest scientific institution of the Soviet Union from 1925 to 1991. It united the country's leading scientists and was subordinated directly to the Council of Ministers of the Soviet Union (un ...

, when the Institute was relocated due to the siege, while on active duty and defended dissertation ''The processes of relaxation of statistical systems and the criterion of mechanical instability'' awarded by the degree of

Doctor of Science A Doctor of Science (; most commonly abbreviated DSc or ScD) is a science doctorate awarded in a number of countries throughout the world. Africa Algeria and Morocco In Algeria, Morocco, Libya and Tunisia, all universities accredited by the s ...

the following year. He then worked at the various Soviet Union's academic institutes, in 1947 together with his supervisor coauthored the Fock-Krylov theorem on quasi-stationary state

decay Decay may refer to: Science and technology * Bit decay, in computing * Decay time (fall time), in electronics * Distance decay, in geography * Software decay, in computing Biology * Decomposition of organic matter * Mitochondrial decay, in g ...

, returned to Leningrad, but fell ill in 1946 and died due to

sepsis Sepsis is a potentially life-threatening condition that arises when the body's response to infection causes injury to its own tissues and organs. This initial stage of sepsis is followed by suppression of the immune system. Common signs and s ...

caused by a

streptococcus ''Streptococcus'' is a genus of gram-positive spherical bacteria that belongs to the family Streptococcaceae, within the order Lactobacillales (lactic acid bacteria), in the phylum Bacillota. Cell division in streptococci occurs along a sing ...

. In 1950, his supervisor Vladimir Fock and fellow student

Arkady Migdal Arkady Beynusovich (Benediktovich) Migdal (; Lida, Russian Empire, 11 March 1911 – Princeton, United States, 9 February 1991) was a Soviet physicist and member of the Academy of Sciences of the Soviet Union. He developed the formula that accou ...

published first chapters of his unfinished monograph started after he returned to Leningrad, text of the Doctor of Science dissertation and a small article, later translated by Migdal along with

Yakov Sinai Yakov Grigorevich Sinai (; born September 21, 1935) is a Russian–American mathematician known for his work on dynamical systems. He contributed to the modern metric theory of dynamical systems and connected the world of deterministic (dynam ...

and published with a help of A. S. Wightman, which contained Fock's biographical note, description of Krylov's theoretical views by both Migdal and Fock. Wightman's preface compared Krylov's ideas to the results by

Poincaré Poincaré is a French surname. Notable people with the surname include: * Henri Poincaré Jules Henri Poincaré (, ; ; 29 April 185417 July 1912) was a French mathematician, Theoretical physics, theoretical physicist, engineer, and philos ...

, Birkhoff, von Neumann, Hopf,

Kolmogorov Andrey Nikolaevich Kolmogorov ( rus, Андре́й Никола́евич Колмого́ров, p=ɐnˈdrʲej nʲɪkɐˈlajɪvʲɪtɕ kəlmɐˈɡorəf, a=Ru-Andrey Nikolaevich Kolmogorov.ogg, 25 April 1903 – 20 October 1987) was a Soviet ...

, Khinchin, and

Wiener Wiener (from German: "Viennese") may refer to: Food * A Vienna sausage of German origin, in German ''Wiener'', named after the capital of Austria * A hot dog, a cooked sausage, traditionally grilled or steamed and served in a sliced bun * A Po ...

, whereas the book was compared by him to the classical books in statistical mechanics by

Maxwell Maxwell may refer to: People * Maxwell (surname), including a list of people and fictional characters with the name ** James Clerk Maxwell, mathematician and physicist * Justice Maxwell (disambiguation) * Maxwell baronets, in the Baronetage of N ...

Boltzmann Ludwig Eduard Boltzmann ( ; ; 20 February 1844 – 5 September 1906) was an Austrian mathematician and theoretical physicist. His greatest achievements were the development of statistical mechanics and the statistical explanation of the seco ...

Gibbs Gibbs or GIBBS is a surname and acronym. It may refer to: People * Gibbs (surname) Places * Gibbs (crater), on the Moon * Gibbs, Missouri, US * Gibbs, Tennessee, US * Gibbs Island (South Shetland Islands), Antarctica * 2937 Gibbs, an asteroid ...

, and

Ehrenfest Ehrenfest is a surname. Notable people with the surname include: *Paul Ehrenfest (1880-1933), Austrian physicist and mathematician **Ehrenfest equations ** Ehrenfest model **Ehrenfest paradox **Ehrenfest theorem **32796 Ehrenfest * Tatjana Ehrenfes ...

and Afanasjewa-Ehrenfest. Thanks to this effort, Krylov's research results had received a permanent place in modern theoretical physics and have laid the foundations of

dynamical systems In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space, such as in a parametric curve. Examples include the mathematical models ...

theory and

Selected publications

* *

References

1917 births 1947 deaths Russian physicists Saint Petersburg State University alumni {{Russia-physicist-stub