Order of the Badge of Honour, twice (1944, 1944).Order of the Red Banner of Labour, twice (1948, 1954).Hero of Socialist Labour, twice (1969, 1979).This work was the first to introduce the notion of time hierarchy in non-equilibrium statistical physics which then became the key concept in all further development of the statistical theory of irreversible processes. In other words, he showed that depending on the choice of the time scale for the corresponding approximations the same stochastic process can be regarded as both dynamical and Markovian, and in the general case as a non-Markov process. In his work a simple example of an anharmonic oscillator driven by a superposition of incoherent sinusoidal oscillations with continuous spectrum was used to show that depending on a specific approximation time scale the evolution of the system can be either deterministic, or a stochastic process satisfying Fokker-Planck equation, or even a process which is neither deterministic nor stochastic.
In the period 1943–1946, Bogolyubov's research was essentially concerned with the theory of stochastic processes and asymptotic methods.
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