论文标题
在具有对称性的机械系统的吉布斯状态上
On Gibbs states of mechanical systems with symmetries
论文作者
论文摘要
法国数学家和物理学家让·玛丽·索里亚（Jean-Marie Souriau）考虑了吉布斯国家对谎言群体对符号歧管的哈密顿作用的国家。在这里介绍了所有既定结果的详细证明。使用伪欧亚人三维矢量空间的跨产品的适应，我们介绍了此类Gibbs状态的几个示例，以及相关的热力学函数，用于各种二维符号歧管，包括伪spheres，包括Pseudo-Spheres，PoincaréDisk和Poincarédisk andpoincaréFallane。
Gibbs states for the Hamiltonian action of a Lie group on a symplectic manifold were studied, and their possible applications in Physics and Cosmology were considered, by the French mathematician and physicist Jean-Marie Souriau. They are presented here with detailed proofs of all the stated results. Using an adaptation of the cross product for pseudo-Euclidean three-dimensional vector spaces, we present several examples of such Gibbs states, together with the associated thermodynamic functions, for various two-dimensional symplectic manifolds, including the pseudo-spheres, the Poincaré disk and the Poincaré half-plane.
