From deterministic dynamics to thermodynamic laws II: Fourier's law and mesoscopic limit equation
Mathematical Physics
2020-01-27 v2 math.MP
Abstract
This paper consider the mesoscopic limit of a stochastic energy exchange model that is numerically derived from deterministic dynamics. The law of large numbers and the central limit theorems are proved. We show that the limit of the stochastic energy exchange model is a discrete heat equation that satisfies Fourier's law. In addition, when the system size (number of particles) is large, the stochastic energy exchange is approximated by a stochastic differential equation, called the mesoscopic limit equation.
Keywords
Cite
@article{arxiv.1908.06219,
title = {From deterministic dynamics to thermodynamic laws II: Fourier's law and mesoscopic limit equation},
author = {Yao Li},
journal= {arXiv preprint arXiv:1908.06219},
year = {2020}
}
Comments
v2: proof is simplified