Mathematical Sciences: Exact Results in Statistical Mechanics

数学科学：统计力学的精确结果

• 批准号: 8903047
• 负责人: Sheldon Goldstein
• 金额: $ 5.2万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-06-01 至 1992-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8903047&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Exact; Results; Statistical

One of the fundamental problems in statistical mechanics is to bridge the gap between macroscopic, phenomenological laws - e.g., hydrodynamical and kinetic equations -and the underlying microscopic description involving interactions between a large number of particles. The delicacy of the problem can be appreciated if we consider that the microscopic laws are (time) reversible while the macroscopic are irreversible (Zermelo's "paradox"). Professor Goldstein plans to continue his investigations into problems- e.g., the derivations of diffusion equations, stochastic behavior, and convergence to equilibrium and the steady state- whose solutions would narrow this gap.

统计力学中的基本问题之一是弥合宏观，现象学定律（例如流体动力学和动力学方程）之间的差距，以及涉及大量粒子之间相互作用的基本微观描述。 如果我们认为显微镜定律是（时间）可逆的，而宏观宏观是不可逆的（Zermelo的“ Paradox”），则可以理解该问题的美味。 戈德斯坦教授计划继续对问题进行调查，例如，扩散方程，随机行为和趋同的衍生物对平衡和稳态 - 其解决方案的差异将缩小这一差距。