A Derivation of the Main Relations of Nonequilibrium Thermodynamics

The principles of nonequilibrium thermodynamics are discussed, using the concept of internal variables that describe deviations of a thermodynamic system from the equilibrium state. While considering the first law of thermodynamics, work of internal variables is taken into account. It is shown that the requirement that the thermodynamic system cannot fulfil any work via internal variables is equivalent to the conventional formulation of the second law of thermodynamics. These statements, in line with the axioms introducing internal variables can be considered as basic principles of nonequilibrium thermodynamics. While considering stationary nonequilibrium situations close to equilibrium, it is shown that known linear parities between thermodynamic forces and fluxes and also the production of entropy, as a sum of products of thermodynamic forces and fluxes, are consequences of fundamental principles of thermodynamics. 1. Introduction The modern nonequilibrium thermodynamics is formulated [1–3] as a generalisation of equilibrium thermodynamics, as adding some concepts and principles, in particular, the concepts of fluxes and thermodynamic forces, specific for non-equilibrium. Despite many different approaches the problem, reviewed recently by Muschik [4], the extension of equilibrium thermodynamics to non-equilibrium thermodynamics seems to need some justification. We are going to follow the approach [5, 6], which exploits additional variables, so-called internal variables,1 to describe deviations of a state of thermodynamic system from equilibrium. It can be thought, that this approach allows one to explore the principles of non-equilibrium thermodynamics, providing some justification of the known linear relations and opens opportunities for nonlinear generalizations. We have to note that formulation of the main principles of non-equilibrium thermodynamics in terms of internal variables is disputable, there is, at least, two explicit versions. In particular, one of the approaches [6] takes into consideration only distinctive internal variables, those that can be called [7] complexity internal variables. The other approach, which is followed in this paper, considers all quantities, which describe the deviation of the system from the equilibrium, to be internal variables. In this paper, we are trying to show advantages of our description [7] as compared with the alternative formulation [4, 6]. Section 2 begins with a description of a set of variables needed for the depiction of a non-equilibrium state of a thermodynamic system. Further, reproducing partly