Symbolic test of the Jacobi identity for given generalized ‘Poisson’ bracket

Abstract
We have developed and provide an algorithm which allows to test the Jacobi identity for a given generalized ‘Poisson’ bracket. Novel frameworks for nonequilibrium thermodynamics have been established, which require that the reversible part of motion of thermodynamically admissible models is described by Poisson brackets satisfying the Jacobi identity in order to ensure the full time-structure invariance of equations of motion for arbitrary function(al)s on state space. For a nonassociative al...

Title of program: jacobi2.0
Catalogue Id: ADOE_v1_0

Nature of problem
The problem is to evaluate single and nested arbitrary generalized Poisson brackets and the cyclic sum of these in order to test the Jacobi identity on a given state space for systems described in terms of discrete or of continuous variables. The Jacobi identity has to be fulfilled for Poisson brackets consistently describing the reversible dynamics of physical systems as desired, e.g., within the framework of nonequilibrium thermodynamics [1-3].

Versions of this program held in the CPC repository in Mendeley Data
ADOE_v1_0; jacobi2.0; 10.1016/S0010-4655(01)00161-8

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)

摘要
本团队研发并提供了一项算法，该算法能够对特定广义的泊松括号进行雅可比恒等式测试。在此基础上，我们构建了新的非平衡热力学框架，该框架要求热力学可接受模型的可逆运动部分由满足雅可比恒等式的泊松括号描述，以确保运动方程在状态空间上任意函数的完全时间结构不变性。为了检验描述物理系统可逆动力学（例如，在非平衡热力学框架内）的泊松括号是否满足雅可比恒等式，需要评估单个和嵌套的任意广义泊松括号及其循环和。
程序名称：jacobi2.0
目录编号：ADOE_v1_0

问题性质
本问题的目标是评估单个和嵌套的任意广义泊松括号及其在给定状态空间上的循环和，以检验描述离散或连续变量的系统的泊松括号是否满足雅可比恒等式。为了实现泊松括号对物理系统可逆动力学的连续描述，雅可比恒等式必须得到满足，例如，在非平衡热力学的框架内。

Mendeley数据中 CPC 仓库中保存的此程序的版本
ADOE_v1_0; jacobi2.0; 10.1016/S0010-4655(01)00161-8

此程序已从贝尔法斯特女王大学（1969-2019年）保存的 CPC 程序库中导入。