Hierarchy of evolution equations for correlations of hard-sphere fluids

Authors

DOI:

https://doi.org/10.15407/dopovidi2022.03.003

Keywords:

BBGKY hierarchy, Liouville hierarchy, correlation function

Abstract

In the communication we discuss an approach to describing the correlations in a system of many hard spheres based on the hierarchy of evolution equations for correlation functions. It is established that the constructed dynamics of correlations underlies the description of the dynamics of both finitely and infinitely many hardspheres governed by the BBGKY hierarchies for reduced distribution functions or reduced correlation functions.

Downloads

Download data is not yet available.

References

Cercignani, C., Gerasimenko, V. I. & Petrina, D. Ya. (2012). Many-particle dynamics and kinetic equations. Amsterdam: Springer.

Petrina, D. Ya. & Gerasimenko, V. I. (1990). Mathematical problems of statistical mechanics of a system of elastic balls. Russ. Math. Surv., 5, No. 3, pp. 153-211. https://doi.org/10.1070/RM1990v045n03ABEH002360

https://doi.org/10.1070/RM1990v045n03ABEH002360

Gallagher, I., Saint-Raymond, L. & Texier, B. (2014). From Newton to Boltzmann: hard spheres and shortrange potentials. Zürich Lectures in Advanced Mathematics (vol. 18). Zürich: EMS Publ. House.

https://doi.org/10.4171/129

Bodineau, T., Gallagher, I., Saint-Raymond, L. & Simonella, S. (2020). Fluctuation theory in the Boltzmann-Grad limit. J. Stat. Phys., 180, pp. 873-895. https://doi.org/10.1007/s10955-020-02549-5

https://doi.org/10.1007/s10955-020-02549-5

Duerinckx, M. & Saint-Raymond, L. (2021). Lenard-Balescu correction to mean-field theory. Probab. Math. Phys., 2, No. 1, pp. 27-69. https://doi.org/10.2140/pmp.2021.2.27

https://doi.org/10.2140/pmp.2021.2.27

Duerinckx, M. (2021). On the size of chaos via Glauber calculus in the classical mean-field dynamics. Commun. Math. Phys., 382, pp. 613-653. https://doi.org/10.1007/s00220-021-03978-3

https://doi.org/10.1007/s00220-021-03978-3

Simonella, S. (2014). Evolution of correlation functions in the hard sphere dynamics. J. Stat. Phys., 155, No. 6, pp. 1191-1221. https://doi.org/10.1007/S10955-013-0905-7

https://doi.org/10.1007/s10955-013-0905-7

Pulvirenti, M. & Simonella, S. (2016). Propagation of chaos and effective equations in kinetic theory: a brief survey. Math. Mech. Complex Syst., 4, No. 3-4, pp. 255-274. https://doi.org/10.2140/memocs.2016.4.255

https://doi.org/10.2140/memocs.2016.4.255

Ivankiv, L. I., Prykarpatsky, Y. A., Samoilenko, V. H. & Prykarpatski, A. K. (2021). Quantum current algebra symmetry and description of Boltzmann type kinetic equations in statistical physics. Symmetry, 13, No. 8, 1452. https://doi.org/10.3390/sym13081452

https://doi.org/10.3390/sym13081452

Gerasimenko, V. I. & Gapyak, I. V. (2014). The non-Markovian Fokker-Planck kinetic equation for a system of hard spheres. Dopov. Nac. akad. nauk Ukr., No. 12, pp. 29-35 (in Ukrainian). https://doi.org/10.15407/dopovidi2014.12.029

https://doi.org/10.15407/dopovidi2014.12.029

Gerasimenko, V. I. & Gapyak, I. V. (2012). Hard sphere dynamics and the Enskog equation. Kinet. Relat. Models., 5, No. 3, pp. 459-484. https://doi.org/10.3934/krm.2012.5.459

https://doi.org/10.3934/krm.2012.5.459

Gerasimenko, V. I. & Gapyak, I. V. (2021). Boltzmann-Grad asymptotic behavior of collisional dynamics. Rev. Math. Phys., 33, 2130001. https://doi.org/10.1142/S0129055X21300016

https://doi.org/10.1142/S0129055X21300016

Gerasimenko, V. & Gapyak, I. (2018). Low-density asymptotic behavior of observables of hard sphere fluids. Adv. Math. Phys., 2018, 6252919. https://doi.org/10.1155/2018/6252919

https://doi.org/10.1155/2018/6252919

Prigogine, I. (1962). Non-equilibrium statistical mechanics. New York: John Wiley & Sons.

Gerasimenko, V. I., Ryabukha, T. V. & Stashenko, M. O. (2004). On the structure of expansions for the BBGKY hierarchy solutions. J. Phys. A: Math. Gen., 37, pp. 9861-9872. https://doi.org/10.1088/0305- 4470/37/42/002

https://doi.org/10.1088/0305-4470/37/42/002

Published

02.07.2022

How to Cite

Gapyak І. ., & Gerasimenko В. . (2022). Hierarchy of evolution equations for correlations of hard-sphere fluids. Reports of the National Academy of Sciences of Ukraine, (3), 3–12. https://doi.org/10.15407/dopovidi2022.03.003