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[Licence| Download | New Version Template] aegw_v1_0.tar.gz(262 Kbytes)
Manuscript Title: Automated symbolic calculations in nonequilibrium thermodynamics
Authors: Martin Kröger, Markus Hütter
Program title: Poissonbracket.nb
Catalogue identifier: AEGW_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 181(2010)2149
Programming language: Mathematica 7.0.
Computer: Any computer running Mathematica 6.0 and later versions.
Operating system: Linux, MacOS, Windows.
RAM: 100 Mb
Keywords: Jacobi identity, reversible dynamics, time structure invariance, degeneracy conditions, program code, Poisson bracket.
PACS: 05, 70.Ln, 02.70.Wz, 05.10.-a.
Classification: 4.2, 5, 23.

Nature of problem:
Testing the Jacobi identity can be a very complex task depending on the structure of the Poisson bracket. The Mathematica notebook provided here solves this problem using a novel symbolic approach based on inherent properties of the variational derivative, highly suitable for the present tasks. As a by product, calculations performed with the Poisson bracket assume a compact form.

Solution method:
The problem is first cast into a form which eliminates the need to perform partial integration for arbitrary functionals at the expense of performing variational derivatives. The corresponding equations are conveniently obtained using the symbolic programming environment Mathematica.

Running time:
For the test cases and most typical cases in the literature, the running time is of the order of seconds or minutes, respectively.