C-star algebras and non-equilibrium statistical mechanics

这个博士研究的目的是发展C-星代数和功能分析方法的量子和经典统计力学的平衡和流体力学的研究。目标是在封闭系统的非平衡统计力学的新兴领域中获得数学上严格的结果，特别是考虑到流体力学方面的最新活动。该研究将寻求理解Boltzmann-Gibbs投影原理，非平衡稳态和流体动力学方程，在流体动力学的各种尺度（欧拉，扩散），在各种类型的多体系统，包括量子和经典晶格和粒子气体。推导哈密顿可逆系统的流体力学是数学物理最重要的开放问题之一，本博士研究旨在在这一方向取得进展。

This PhD research aims at developing C-star algebra and functional-analytic methods for the study of quantum and classical statistical mechanics out of equilibrium and hydrodynamics. The goal is to obtain mathematically rigorous results in the emergent fields of the non-equilibrium statistical mechanics of closed systems, especially in view of recent activity in the context of hydrodynamics. The research will look for understanding the Boltzmann-Gibbs projection principle, non-equilibrium steady states, and the hydrodynamic equations, at the various scales of hydrodynamics (Euler, diffusive), in many-body systems of various types including quantum and classical lattices and gases of particles. Deriving hydrodynamics for Hamiltonian, reversible systems is one of the most important open problems of mathematical physics, and this PhD research aims at making progress in this direction.