The thermodynamic hamiltonian for open systems

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 used. A global and statistical approach have been introduced starting from non-equilibrium thermodynamics, obtaining the principle of maximum entropy generation for the open systems. This principle 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. It follows that the irreversibility seems to be the fundamental phenomenon which drives the evolution of the states of the open systems.