Conservation laws in nonlinear dissipative systems (Q2564382)

The possibility of enclosing Hamiltonian theory in a wider context by use of Gibbs-Falkian thermodynamical methods, offering the opportunity to cover mechanical and thermodynamical systems with the same mathematical tools, is considered. Consequently it is shown how Noether's identity can be extended to dissipative systems which are appropriate to describe real life phenomena. By use of the principle of least action, an extended version of Noether's theorem is calculated, from which the conservation of linear momentum and total energy can be derived. Additionally, the condition of absolute invariance is shown to be too restrictive for physical applications.