Automated symbolic calculations in nonequilibrium thermodynamics

We cast the Jacobi identity for continuous fields into a local form which eliminates the need to perform any partial integration to the expense of performing variational derivatives. This allows us to test the Jacobi identity definitely and efficiently and to provide equations between different components defining a potential Poisson bracket. We provide a simple MathematicaTM notebook which allows to perform this task conveniently, and which offers some additional functionalities of use within the framework of nonequilibrium thermodynamics: reversible equations of change for fields, and the conservation of entropy during the reversible dynamics.Program summaryProgram title: Poissonbracket.nbCatalogue identifier: AEGW_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGW_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 227 952No. of bytes in distributed program, including test data, etc.: 268 918Distribution format: tar.gzProgramming language: MathematicaTM 7.0Computer: Any computer running MathematicaTM 6.0 and later versionsOperating system: Linux, MacOS, WindowsRAM: 100 MbClassification: 4.2, 5, 23Nature of problem: Testing the Jacobi identity can be a very complex task depending on the structure of the Poisson bracket. The MathematicaTM 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 MathematicaTM.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.