Macroscopic Diffusion from a Hamilton-like Dynamics

作者：Lefevere Raphael^*

来源：Journal of Statistical Physics, 2013, 151(5): 861-869.

DOI：10.1007/s10955-013-0738-4

• Macroscopic diffusion
• Microscopic Hamilton dynamics
• Irreversibility

We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of Hamiltonian dynamics in a confined phase space: it is deterministic, periodic, reversible and conservative. Randomness enters the model as a way to model ignorance about initial conditions and interactions between the components of the system. The orbits of the particles are non-intersecting random loops. We prove, by a weak law of large number, the validity of a diffusion equation for the macroscopic observables of interest for times that are arbitrary large, but small compared to the minimal recurrence time of the dynamics.

• 出版日期2013-6