| Summary: | 碩士 === 國立暨南國際大學 === 土木工程學系 === 91 === Thermodynamic is an important groundwork of theorical physics. There are many thermodynamical techniques discussed ardently in mechanics. Research of equilibrium thermodynamic has been developed completely by previous scholars. The problems of non-equilibrium thermodynamic and dissipative systems have been understood gradually in recent years. Some techniques dealing with solving non-equilibrium thermodynamic problems have been proposed in succession. Bracket formalism which we discuss in this article is one of the techniques solving non-equilibrium thermodynamic problems.
There are existing Poisson bracket structures which are corresponding to the Hamiltonian structures whether in classical mechanics systems or in quantum mechanics systems. The Poisson bracket structure originally developed for the discrete particle systems. In order to apply the Poisson bracket structure to the continuum systems, we would generalize the Poisson bracket structure by coordinate transforming technique (transformation from Lagrangian coordinate to Eulerian coordinate).
In previous studies, some generalized Poisson brackets of basic standard thermodynamics systems have been proposed by coordinate transforming technique. In this article, we also use coordinate transforming technique to achieve the generalized Poisson brackets of the electro- and magneto-hydrodynamics system, mixture system, nonlinear elasticity system, entropy fluid system and MR fluid system. When we solve various forms of problems of standard thermodynamics systems and generalized thermodynamics systems by coordinate transforming technique, at the same time, the huge power of the coordinate transforming technique is easily illustrated.
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