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Symbolic Test of the Jacobi Identity for Given Generalized 'Poisson' Bracket

Martin Kröger
Organization: ETH Zürich, Institute of Polymers, Zürich, and Technische Universitat, Berlin
Markus Hütter
Organization: ETH Zürich, Institute of Polymers, Zürich
Hans Christian Öttinger
Organization: ETH Zürich, Institute of Polymers, Zürich
Journal / Anthology

Computer Physics Communications
Year: 2001
Volume: 137
Page range: 325-340

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].

*Mathematics > Algebra > Linear Algebra
*Science > Physics > Thermodynamics and Statistical Mechanics

Jacobi identity, Poisson brackets, GENERIC, nonequilibrium thermodynamics, reversible motion, symbolic programming