In this study we develop a systematic procedure to construct a Poisson operator that describes the dynamics of a three dimensional nonholonomic system. Instead of reducing by symmetry the antisymmetric operator that links the energy gradient to the velocity on the tangent bundle, the system is embedded in a larger space. Here, the extended antisymmetric operator, which preserves the original equations of motion, satisfies the Jacobi identity in a conformal fashion. Thus, a Poisson operator can be obtained by a further time reparametrization. Such Poissonization does not rely on the specific form of the Hamiltonian function. The theory is applied to calculate the equilibrium distribution function of a non-Hamiltonian ensemble.

中文翻译：

---

具有不可积拓扑约束的统计力学：打结相空间中的自组织

在这项研究中，我们开发了一个系统的程序来构造一个泊松算子，该算子描述了三维非完整系统的动力学。系统不是通过对称来减少将能量梯度与切丛上的速度联系起来的反对称算子，而是将系统嵌入到更大的空间中。这里，保留原始运动方程的扩展反对称算子以保形方式满足雅可比恒等式。因此，可以通过进一步的时间重新参数化获得泊松算子。这种泊松化不依赖于哈密顿函数的特定形式。该理论用于计算非汉密尔顿系综的平衡分布函数。