The Gouy-Stodola theorem as a variational principle for open systems.

Abstract

The variational method is very important in mathematical and theoretical physics because it allows us to describe the natural systems by physical quantities independently from the frame of reference. A global and statistical approach is introduced starting from irreversible thermodynamics to obtain the principle of maximum entropy generation for the open systems. The recent research in non equilibrium and far from equilibrium systems have been proved to be useful for their applications in different disciplines and many subjects. A general principle to analyse all these phenomena is required in science and engineering: a variational principle would have this fundamental role. Here, the Gouy-Stodola theorem is proposed to be this general variational principle, both proving that it satisfies the above requirements and relating it to a statistical results on entropy production. The result is a consequence of the Lagrangian approach to the open systems. Here it will be developed a general approach to obtain the thermodynamic Hamiltonian for the dynamical study of the open systems. Last the algebraic-geometrical structure for entropy generation is also introduced.