自治统计系统闭包的路径积分形式
A path integral formalism for the closure of autonomous statistical systems
摘要：
最近作者提出了一种路径积分形式，它给出了哈密顿统计系统中慢变量矩的时间演化。这种封闭依赖于评估一个时间序列（路径）的近似密度从刘维进化，一个确切的密度必须遵循的信息差异。然后使用广义玻尔兹曼原理将差异用于加权所有可能的路径。该形式主义在这里扩展到处理更一般和现实的自治动力系统。在那里，动力学变量的时间导数的发散不需要像在哈密顿的情况下那样消失，并且这个属性使封闭推导变得复杂。许多有趣的和现实的应用所涵盖的这种新的形式主义，包括那些描述现实的湍流和这种情况的相关细节的概述。与实施概述的形式主义的实际问题进行了讨论。
英文摘要：
Recently a path integral formalism has been proposed by the author which gives the time evolution of moments of slow variables in a Hamiltonian statistical system. This closure relies on evaluating the informational discrepancy of a time sequence (path) of approximating densities from the Liouvillian evolution that an exact density must follow. The discrepancy is then used to weight all possible paths using a generalized Boltzmann principle. That formalism is extended here to deal with more general and realistic autonomous dynamical systems. There the divergence of the time derivative of dynamical variables need not vanish as it does in the Hamiltonian case and this property complicates the closure derivation. Many interesting and realistic applications are covered by this new formalism including those describing realistic turbulence and the relevant specifics of this situation are outlined. The practical issues associated with the implementation of the outlined formalism are also discussed.
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