We are not able to resolve this OAI Identifier to the repository landing page. If you are the repository manager for this record, please head to the Dashboard and adjust the settings.
The original paper has been split in two parts with some new material and correctionsWe discuss the dynamics and thermodynamics of systems with long-range interactions. We contrast the microcanonical description of an isolated Hamiltonian system to the canonical description of a stochastically forced Brownian system. We show that the mean-field approximation is exact in a proper thermodynamic limit. The equilibrium distribution function is solution of an integrodifferential equation obtained from a static BBGKY-like hierarchy. It also optimizes a thermodynamical potential (entropy or free energy) under appropriate constraints. We discuss the kinetic theory of these systems. In the Nâ+â limit, a Hamiltonian system is described by the Vlasov equation. To order 1/N, the collision term of a homogeneous system has the form of the Lenard-Balescu operator. It reduces to the Landau operator when collective effects are neglected. We also consider the motion of a test particle in a bath of field particles and derive the general form of the Fokker-Planck equation. The diffusion coefficient is anisotropic and depends on the velocity of the test particle. This can lead to anomalous diffusion. For Brownian systems, in the Nâ+â limit, the kinetic equation is a non-local Kramers equation. In the strong friction limit Οâ+â, or for large times tâ«ÎŸâ1, it reduces to a non-local Smoluchowski equation. We give explicit results for self-gravitating systems, two-dimensional vortices and for the HMF model. We also introduce a generalized class of stochastic processes and derive the corresponding generalized Fokker-Planck equations. We discuss how a notion of generalized thermodynamics can emerge in complex systems displaying anomalous diffusion
Is data on this page outdated, violates copyrights or anything else? Report the problem now and we will take corresponding actions after reviewing your request.