自引力体系的平衡态统计力学

The equilibrium statistical mechanics of self-gravitating.has not been successfully established for more than 50 years. With a series of works, the current applicant has set up a self-consistent theoretical framework of this statistical mechanics. The main points are the following: for self-gravitating systems, (1) both the concept of entropy and the entropy principle are still valid, but the maximum entropy principle is invalid; (2) the equilibrium states are the joint mechanical and statistical equilibrium state, the latter of which is not the maximum, but the saddle-point entropy state; (3) ergodicity is invalid globally, but can be re-established locally for self-gravitating systems; (4) the Boltzmann-Gibbs statistics is still valid for self-gravitating systems; (5) besides the usual mass and energy conservations, the series of virial equations should be included as additional constraints to the entropy functional. The statistical mechanics of self-gravitating systems is the inter-discipline of both astrophysics and statistical physics. If this statistical mechanics is finished, there will be a unified physical origin for most of the empirical relationships of dark matter halos, revealed by cosmological N-body simulations. Moreover, the equilibrium statistical mechanics of self-gravitating systems will also boost the progress of statistical physics of other long-range interaction systems. Based on the series of works already finished by the current applicant, this project will further contributes to the development of the equilibrium statistical mechanics of self-gravitating systems through N-body simulations and analytical studies for self-gravitating systems.

自引力体系平衡态统计力学，历经五十多年，迄今没能很好地发展起来。经过将近四年的研究，申请者完成了系列工作，并构建了一个自洽的自引力体系平衡态统计力学的理论框架，其重要创新点是：对于自引力体系，（1）熵的概念和熵原理仍然成立，但最大熵原理不再有效；（2）其平衡态是力学平衡和统计平衡的联合平衡态，但不是最大熵态，而是鞍点熵态；（3）各态历经性全局不成立，但可以局域地确立起来；（4）Boltzmann-Gibbs统计对于自引力体系依然成立；（5）系列维里方程是熵泛函的附加约束。自引力体系平衡态统计力学是天体物理学和统计物理学的交叉学科。如果这门统计力学能够完成，则宇宙学数值模拟所发现的众多暗物质晕的经验关系，将会有统一的物理起源，并且也必将会促进其他长程力体系统计物理的发展。本项目在已有工作的基础上，以N-体数值模拟和解析研究的方法，进一步推进自引力体系平衡态统计力学的发展。

自引力体系平衡态统计力学，历经五十多年，迄今没能很好地发展起来。经过将近四年的研究，申请者完成了系列工作，并构建了一个自洽的自引力体系平衡态统计力学的理论框架，其重要创新点是：对于自引力体系，（1）熵的概念和熵原理仍然成立，但最大熵原理不再有效；（2）其平衡态是力学平衡和统计平衡的联合平衡态，但不是最大熵态，而是鞍点熵态；（3）各态历经性全局不成立，但可以局域地确立起来；（4）Boltzmann-Gibbs统计对于自引力体系依然成立；（5）系列维里方程是熵泛函的附加约束。自引力体系平衡态统计力学是天体物理学和统计物理学的交叉学科。如果这门统计力学能够完成，则宇宙学数值模拟所发现的众多暗物质晕的经验关系，将会有统一的物理起源，并且也必将会促进其他长程力体系统计物理的发展。本项目在已有工作的基础上，以N-体数值模拟和解析研究的方法，进一步推进自引力体系平衡态统计力学的发展。