CONSERVATION-LAWS IN NONLINEAR DISSIPATIVE SYSTEMS

In Hamiltonian theory, Noether's theorem commonly is used to show the conservation of linear momentum and energy as a consequence of symmetr y properties. The possibility of enclosing Hamiltonian theory in a wid er context by use of Gibbs-Falkian thermodynamical methods, offering t he opportunity to cover mechanical and thermodynamical systems with th e same mathematical tools, is considered. Consequently it is shown how Noether's identity can be extended for dissipative systems which are appropriate to describe real life phenomena. By use of the principle o f least action an extended version of Noether's theorem is calculated, from which the conservation of linear momentum and total energy can b e derived. Additionally, the condition of absolute invariance is shown to be too restrictive for physical applications.