Fourier's Law from Deterministic Particle Systems


Yao Li, Department of Mathematics and Statistics, University of Massachusetts Amherst


2019.06.28 10:00-11:00


Room 306, No. 5 Science Building


The derivation of Fourier’s law from microscopic Hamiltonian dynamics, which means the energy flux is proportional to the temperature gradient, is a century-old challenge to mathematicians and physicists. In this talk, I will discuss how to derive Fourier’s law from a deterministic particle system. Consider many gas particles in a long and thin tube interacting through elastic collisions. We first derive a stochastic energy exchange model through numerical computations. Many rigorous justifications can then be made for this stochastic model. In particular, I will show that the energy profile of this energy exchange model satisfies the law of large number and the central limit theorem at the mesoscopic limit. Fourier’s law is satisfied when taking such a mesoscopic limit.