Propagation processes of correlations of hard spheres
arXiv:2111.13940 · doi:10.1007/s10955-022-02958-8
Abstract
The paper develops an approach to the description of the evolution of correlations for many hard spheres based on a hierarchy of evolution equations for the cumulants of the probability distribution function governed by the Liouville equation. It is established that the constructed dynamics of correlations underlies the description of the evolution of the states of many hard spheres described by the BBGKY hierarchy for reduced distribution functions or the hierarchy of nonlinear evolution equations for reduced correlation functions. As an application of the developed approach to describing the evolution of the state of many hard spheres within the framework of dynamics of correlations, the challenges of the derivation of kinetic equations are discussed.
arXiv comment26 pages. arXiv admin note: substantial text overlap with arXiv:2012.03001
References in corpus (8)
- The Boltzmann-Grad Limit of a Hard Sphere System: Analysis of the Correlation Error
- On the size of chaos via Glauber calculus in the classical mean-field dynamics
- On Rigorous Derivation of the Enskog Kinetic Equation
- Fluctuation theory in the Boltzmann--Grad limit
- Dynamics of Correlations of Bose and Fermi Particles
- The von Neumann Hierarchy for Correlation Operators of Quantum Many-Particle Systems
- Lenard-Balescu correction to mean-field theory
- The Boltzmann-Grad asymptotic behavior of collisional dynamics: a brief survey