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

## Description

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)