Extended thermodynamics in a discrete-system approach

The foundation of non-equilibrium thermodynamics is discussed. The behaviour of thermodynamic systems is described with the help of internal variables. It is shown that the requirement that a thermodynamic system cannot fulfil any work via internal variables is equivalent to the conventional formulation of the second law of thermodynamics. This work has to be included into the balance energy equation (the first law of thermodynamics). These statements, in line with axioms introducing internal variables, can be considered as basic principles of non-equilibrium thermodynamics. The statements do not affect equilibrium thermodynamic functions, but allow one to obtain consistent definitions of non-equilibrium functions. On some examples, it is demonstrated that the developed formalism provides the known results for non-equilibrium functions in a direct way, which encourages us to investigate and apply the formalism further