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.

统计力学的基本问题之一 是弥合宏观现象学定律之间的差距 - 例如，在一个实施例中，流体动力学和动力学方程， 涉及相互作用的潜在微观描述 大量的粒子之间。 的微妙 如果我们考虑到微观的， 法律是（时间）可逆的，而宏观的是 Zermelo的悖论（paradox）。 戈尔茨坦教授计划 继续他对问题的调查-例如，的 扩散方程的推导，随机行为， 收敛到平衡和稳定状态-其 解决办法将缩小这一差距。