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Article overview
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Non-commutative Geometry and Kinetic Theory of Open Systems | | A. Dimakis
; C. Tzanakis
; | | Date: |
8 Aug 1995 | | Journal: | J.Phys. A29 (1996) 577-594 | | Subject: | hep-th | | Abstract: | The basic mathematical assumptions for autonomous linear kinetic equations for a classical system are formulated, leading to the conclusion that if they are differential equations on its phase space $M$, they are at most of the 2nd order. For open systems interacting with a bath at canonical equilibrium they have a particular form of an equation of a generalized Fokker-Planck type. We show that it is possible to obtain them as Liouville equations of Hamiltonian dynamics on $M$ with a particular non-commutative differential structure, provided certain geometric in character, conditions are fulfilled. To this end, symplectic geometry on $M$ is developped in this context, and an outline of the required tensor analysis and differential geometry is given. Certain questions for the possible mathematical interpretation of this structure are also discussed. | | Source: | arXiv, hep-th/9508035 | | Services: | Forum | Review | PDF | Favorites | |
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