The BBGKY Hierarchy and Fokker-Planck Equation for Many-Body Dissipative Randomly Driven Systems
arXiv:1412.6652 · doi:10.1063/1.4918612
Abstract
By generalizing Bogolyubov's reduced description method, we suggest a formalism to derive kinetic equations for many-body dissipative systems in external stochastic field. As a starting point, we use a stochastic Liouville equation obtained from Hamilton's equations taking dissipation and stochastic perturbations into account. The Liouville equation is then averaged over realizations of the stochastic field by an extension of the Furutsu-Novikov formula to the case of a non-Gaussian field. As the result, a generalization of the classical Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy is derived. In order to get a kinetic equation for the one-particle distribution function, we use a regular cut off procedure of the BBGKY hierarchy by assuming weak interaction between the particles and weak intensity of the field. Within this approximation we get the corresponding Fokker-Planck equation for the system in a non-Gaussian stochastic field. Two particular cases by assuming either Gaussian statistics of external perturbation or homogeneity of the system are discussed.
References in corpus (20)
- Traffic and Related Self-Driven Many-Particle Systems
- Statistical Physics of Vehicular Traffic and Some Related Systems
- The Mechanics and Statistics of Active Matter
- Active Brownian Particles. From Individual to Collective Stochastic Dynamics
- Dynamical density functional theory for interacting Brownian particles: stochastic or deterministic?
- Randomly Driven Granular Fluids: large scale structure
- Randomly Driven Granular Fluids: collisional statistics and short scale structure
- Boltzmann-Ginzburg-Landau approach for continuous descriptions of generic Vicsek-like models
- Kovacs-like memory effect in driven granular gases
- Self-propelled particles with selective attraction-repulsion interaction - From microscopic dynamics to coarse-grained theories
- Granular gases: dynamics and collective effects
- Brownian particles with long and short range interactions
- What is the temperature of a granular medium?
- Linear hydrodynamics for driven granular gases
- Fluctuating hydrodynamics for driven granular gases
- Towards a quantitative kinetic theory of polar active matter
- Transport coefficients for driven granular mixtures at low-density
- Stochastic model for the dynamics of interacting Brownian particles
- Comment on Ihle, "Towards a quantitative kinetic theory of polar active matter"
- Reply to comment on "Towards a quantitative kinetic theory of polar active matter" by Bertin et al