Problems in the statistical theory of open systems: Criteria for the relative degree of order in self-organization processes

The aim of this paper is to examine two problems in the statistical theory of open systems, namely, (1) the connection between statistical and dynamic descriptions of motion in open systems, and the constructive positive role of dynamic instability in atomic motion as a basis for kinetic equations and (2) the different criteria for the relative degree of order in nonequilibrium states of open systems, namely, K-entropy, the Lyapunov function, and the Boltzmann--Gibbs--Shannon entropy renormalized to given mean effective energy (S-theorem). It is shown that the S-theorem can be used to determine the relative degree of order from experimental data on empirical realizations of leading characteristics for different values of control parameters.

PACS: 05.40.Jc, 05.70.Ln, 05.70.Ce, 05.45.Xt (all)
DOI: 10.1070/PU1989v032n05ABEH002717
URL: https://ufn.ru/en/articles/1989/5/b/
Citation: Klimontovich Yu L "Problems in the statistical theory of open systems: Criteria for the relative degree of order in self-organization processes" Sov. Phys. Usp. 32 416–433 (1989)

BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Оригинал: Климонтович Ю Л «Проблемы статистической теории открытых систем: критерии относительной степени упорядоченности состояний в процессах самоорганизации» УФН 158 59–91 (1989); DOI: 10.3367/UFNr.0158.198905b.0059

Cited by (43) Similar articles (20) ↓

Yu.L. Klimontovich “Nonlinear Brownian motion” Phys. Usp. 37 737–766 (1994)
M.I. Rabinovich “Stochastic self-oscillations and turbulence” Sov. Phys. Usp. 21 443–469 (1978)
Yu.L. Klimontovich, V.P. Silin “The spectra of systems of interacting particles and collective energy losses during passage of charged particles through matter” Sov. Phys. Usp. 3 84–114 (1960)
A.S. Monin “On the nature of turbulence” Sov. Phys. Usp. 21 429–442 (1978)
Yu.L. Klimontovich “Problems of statistical theory of interaction of atoms with radiation” Sov. Phys. Usp. 13 480–494 (1971)
Yu.L. Klimontovich “Physics of collisionless plasma” Phys. Usp. 40 21–51 (1997)
V.I. Klyatskin, V.I. Tatarskii “Diffusive random process approximation in certain nonstationary statistical problems of physics” Sov. Phys. Usp. 16 494–511 (1974)
V.M. Zhdanov, V.I. Roldugin “Non-equilibrium thermodynamics and kinetic theory of rarefied gases” Phys. Usp. 41 349–378 (1998)
A.V. Khomenko, I.A. Lyashenko “Statistical theory of the boundary friction of atomically flat solid surfaces in the presence of a lubricant layer” Phys. Usp. 55 1008–1034 (2012)
A.M. Glezer, R.V. Sundeev et al “Physics of severe plastic deformation” Phys. Usp. 66 32–58 (2023)
Yu.L. Klimontovich, A.S. Kovalev, P.S. Landa “Natural fluctuations in lasers” Sov. Phys. Usp. 15 95–113 (1972)
Yu.L. Klimontovich “Kinetic equations for nonideal gas and nonideal plasma” Sov. Phys. Usp. 16 512–528 (1974)
A.I. Olemskoi, I.V. Koplyk “The theory of spatiotemporal evolution of nonequilibrium thermodynamic systems” Phys. Usp. 38 1061–1097 (1995)
V.K. Vanag “Study of spatially extended dynamical systems using probabilistic cellular automata” Phys. Usp. 42 413–434 (1999)
Yu.G. Rudoi, A.D. Sukhanov “Thermodynamic fluctuations within the Gibbs and Einstein approaches” Phys. Usp. 43 1169–1199 (2000)
V.V. Klinshov, V.I. Nekorkin “Synchronization of delay-coupled oscillator networks” Phys. Usp. 56 1217–1229 (2013)
V.N. Ryzhov, E.E. Tareyeva et al “Berezinskii—Kosterlitz—Thouless transition and two-dimensional melting” Phys. Usp. 60 857–885 (2017)
G.I. Strelkova, V.S. Anishchenko “Spatio-temporal structures in ensembles of coupled chaotic systems” Phys. Usp. 63 145–161 (2020)
A.E. Hramov, N.S. Frolov et al “Functional networks of the brain: from connectivity restoration to dynamic integration” Phys. Usp. 64 584–616 (2021)
L.M. Martyushev “Мaximum entropy production principle: history and current status” Phys. Usp. 64 558–583 (2021)

The list is formed automatically.