Structure of variational principles in nonequilibrium thermodynamics

There are a lot of different methods to construct variational principles in physics. In this paper we investigate and classify some of the known methods, focusing our treatment mainly on the variational principles in nonequilibrium thermodynamics. This area of physics is remarkably rich in different variational methods, because here we cannot obtain a classical, Hamiltonian variational principle for the transport equations, as far as if we consider them in their original form and with their original variables.