Statistical Description of Non-Equilibrium Many-Particle Systems


  • B.I. Lev Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine
  • A.G. Zagorodny Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine



non-equilibrium statistical operator, many-particle systems, stationary states


In most cases, the systems of interacting particles are non-equilibrium. In this review, a new approach based on the application of a non-equilibrium statistical operator is presented, which allows the inhomogeneous distributions of the particles and the temperature to be taken into account. The method uses the saddle-point procedure to find dominant contributions to the partition function of the system and enables all of its thermodynamic parameters to be determined. Probable peculiarities in the behavior of the systems with interaction – such as gravitational systems, systems with Coulombic repulsion, and so forth – under various thermodynamic conditions are predicted. A new approach is proposed to describe non-equilibrium systems in the energy space, which is an extension of the Gibbs approach to macroscopic systems under non-equilibrium conditions. It allows the stationary states and the dynamics of non-equilibrium systems to be described.


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How to Cite

Lev, B., & Zagorodny, A. (2020). Statistical Description of Non-Equilibrium Many-Particle Systems. Ukrainian Journal of Physics, 65(12), 1056.



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